# Heights & Distances Questions and Answers

Geometry

Heights & Distances8 Use the figure to answer the following 2 points a What is the measure of the shortest side of the sail on the model Round your answer to the nearest tenth b What is the measure of the longest side Round your answer to the nearest tenth B MAM 9 What is the area of the given triangle Round to the 10 A local park is located on a triangular piece of land nearest tenth 1 point What is the area of the park to the nearest tenth 1 point A 13 cm 7 cm 38 C R 75 m E60 40 28 in 150 m Checkpoint Score Total 11 15

Geometry

Heights & Distancesb Solve the triangle by finding the length of DF and the measures of all the angles For side lengths round to the nearest tenth For angles round to the nearest degree 2 points a DF LE 2F 7 Find all the missing side lengths for the following triangles 3 points 2 V U 30 5 3 2 60 b 2 2 d b D F 45 a 5 ft E 5 83 ft 7 4 m 45 n

Geometry

Heights & DistancesHW 2 1 What values of u and v are correct for the following 45 45 90 right triangle 10 A u 45 D u B C u 10 2 10 6 10 6 v 10 3 u 10 2 v 10 2 v 10 v 10 45 X 11 3 3 Find the missing side lengths Leave your answers as radicals in simplest form m work Complete problems 1 6 below for independent practice 14 When you are finished check the solutions with your teacher 5 Find the missing side lengths Leave your answers as radicals in simplest form 60 y 2 What values of a and b are correct for the following 30 60 90 right triangle 30 A a 34 b 17 3 B a 17 3 b 34 68 3 C a 3 D a 34 b 17 6 4 Find the missing side lengths Leave your answers as radicals in simplest form 16 45 16 17 6 Find the missing side lengths Leave your answers as radicals in simplest form y 30 b 17 6 Optional Complete problems 3 10 18 22 your textbook on separate lined paper

Geometry

Heights & Distances1 mzY Love 2 mzz lifelong LEARNING to the nearest degree Geometry A alla staminoghT 23 AOTHAOHO2 14 Credit 5 ZL4L Geometry A 2020 Page 123

Geometry

Heights & DistancesS 4 Consider a rectangular box with one of the vertics at the origin and point A 2 3 5 as shown Determine the angle between BC and BA Round to the nearest degree ZA B A 2 3 5 C

Geometry

Heights & DistancesNate heard stories about the massive Sierra redwoods in California and looked forward to seeing one of these trees for himself On his first actual encounter with one of the trees Nate wants to know just how tall the tree is He places a mirror on the ground and experiments several times until he determines the correct distance from the base of the tree as well as the correct angle of incidence that allows him to see the top of the tree 1 9 m

Geometry

Heights & DistancesIn an isosceles triangle ABC with AB AC the bisector of angle C meets side AB at D if BC AC AD then A ZA B C T 3 3 8 C length of angle bisector CD 4 2 2 AB cos D length of angle bisector CD 4 2 2 AB cos RO ROO 8 TC 8 N REDMI 7 CAMERA

Geometry

Heights & DistancesA hot air balloon is floating above a straight road To calculate their height above the ground the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon The angles of depression are found to be 16 and 19 How high in feet is the ballon Hint

Geometry

Heights & DistancesMatch the following drawings with the fitting s you would use 14 90 elbow a 15 Wye 45 b 16 45 elbow 45 elbow C 17 4 0 Wye d

Geometry

Heights & Distances1 Use the given values to evaluate if possible three trigonometric functions cos x csc x tan x 1 sin x cos x 0

Geometry

Heights & Distances2 Use the given values to evaluate if possible two trigonometric functions tan and csc w cot 5 sin w 10

Geometry

Heights & Distances20 Which triangles are similar to triangle ABC where Angle A is 70 degree and angle C is 10 degrees A Triangle DEF where D is 70 degrees and F is 10 degree B Triangle GHI where G is 70 degree and H is 10 degree C Triangle JKL where K is 100 degree and L is 10 degree D Triangle MNO where M is 70 degree and N is 100 degree

Geometry

Heights & DistancesThe Lewis Broadcasting Tower in Columbus Georgia is approximately 1 tall If you are on level ground exactly 5280 feet one mile from ba tower what is your angle of elevation looking up at the top of the towe answer in degrees Oal 14 0 Ob 14 4 Od 76 0 d 43 5

Geometry

Heights & DistancesA hot air balloon is floating above a straight road To estimate their height above the ground the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon The angles of depression are for to be 22 and 24 How high is the balloon O 46 104 ft O 11 526 ft O 23 052 ft

Geometry

Heights & DistancesA passenger in an airplane at an altitude of a 30 kilometers sees two towns directly to the east of the plane The angles of depression to the towns are 28 and 55 see figure How far apart are the towns How far apart are the ships Round your answer to one decimal place a km 55 28 88 Not drawn to sale

Geometry

Heights & DistancesFind the exact values of sin u 2 cos u 2 and tan u 2 using the half angle formulas cot u 3 u 3 2 sin u 2 cos u 2 tan u 2

Geometry

Heights & DistancesA Given AAEF is isosceles D is midpoint AF Prove ZAED FED E D F Statement Reason

Geometry

Heights & DistancesDetermine the remaining sides and angles of the triangle ABC where A 118 45 B 37 95 and b 120 feet C 23 6 www a feet Do not round until the final answer Then round to the nearest tenth as needed

Geometry

Heights & DistancesThe lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 17 days About what percentage of births would be expected to occur within 51 days of the mean pregnancy length About of births would be expected to occur within 51 days of the mean pregnancy length Type an integer or a decimal Round to two decimal places as needed

Geometry

Heights & DistancesACCVIV clity to record the Description Common Shares Contributed Surplus Retained Earnings Cash COMING SHIGES Earnings Per Share Revenue Debt to Equity Ratio Debit 5 040 000 545 000 7 015 000 Credit 12 600 000 Place only one T in each row below indicating the impact of the share reacquisition journal entry on the following financial statement metrics Positive Negative Not No Impact Determinable

Geometry

Heights & DistancesACCVIV clity to record the Description Common Shares Contributed Surplus Retained Earnings Cash COMING SHIGES Earnings Per Share Revenue Debt to Equity Ratio Debit 5 040 000 545 000 7 015 000 Credit 12 600 000 Place only one T in each row below indicating the impact of the share reacquisition journal entry on the following financial statement metrics Positive Negative Not No Impact Determinable

Geometry

Heights & DistancesIn the diagram below OP is parallel to LM If OP is 7 more than LO ON 10 and LM 18 find the length of LO Figures are not necessarily drawn to scale State your answer in simplest radical form if necessary

Geometry

Heights & DistancesHome Properties is developing a subdivision that includes 330 home lots The 210 lots in the Canyon section are below a ridge and do not have views of the neighboring canyons and hills the 120 lots in the Hilltop section offer unobstructed views The expected selling price for each Canyon lot is 44 000 and for each Hilltop lot is 102 000 The developer acquired the land for 1 600 000 and spent another 3 800 000 on street and utilities improvements Assign the joint land and improvement costs of 5 400 000 to the Canyon section and the Hilltop section using the value basis of allocation Note Do not round your intermediate calculations Canyon section Hilltop section Totals Sales Value Numerator Percent of Sales Value Denominator of Sales Value Cost to Allocate Allocated Cost

Geometry

Heights & DistancesA hot air balloon is floating above a straight road To calculate their height above the ground the balloonists simultaneously measure the angle of depression t two consecutive mileposts on the road on the same side of the balloon The angles of depression are found to be 17 and 20 How high in feet is the ballon G

Geometry

Heights & DistancesAn aerial photograph from a U 2 spy plane is taken of a building suspected of housing nuclear warheads When the photograph is taken the angle of elevation of the sun is 33 By comparing the shadow cast by the building in question to the shadows of other objects of known size in the photograph scientists determine that the shadow of the building in question is 72 feet long How tall is the bulding Round your answer to two decimal places feet

Geometry

Heights & DistancesAllocation of overhead Supervision expenses Materials Personnel Manufacturing Packaging Totals Utilities Materials Personnel Manufacturing Packaging Totals Insurance Materials Personnel Manufacturing Packaging Totals Allocation Base Number of employees Number of employees Number of employees Number of employees Allocation Base Square feet occupied Square feet occupied Square feet occupied Square feet occupied Allocation Base Asset values Asset values Asset values Asset values of allocation base Numerator 28 7 63 42 140 Cost to be Denominator of Total allocated 39000 6500 65000 19500 130000 140 140 140 140 of allocation base Cost to be Numerator Denominator of Total allocated 130000 130000 130000 130000 12 600 00 63 000 00 3 150 00 63 000 00 31 500 00 63 000 00 15 750 00 63 000 00 63 000 00 Allocated 20 82 800 00 16 560 00 5 82 800 00 4 140 00 45 82 800 00 37 260 00 30 82 800 00 24 840 00 82 800 00 of allocation base Cost to be Numerator Denominator of Total allocated cost Allocated cost 30 53 000 00 15 900 00 5 53 000 00 2 650 00 50 53 000 00 26 500 00 15 53 000 00 7 950 00 53 000 00 Allocated cost 20 24 000 00 4 800 00 5 24 000 00 1 200 00 50 24 000 00 12 000 00 25 24 000 00 6 000 00 24 000 00

Geometry

Heights & DistancesGraph the following ellipse Give the domain range center vertices endpoints of the minor axis and foci 9x y 225 The center of the ellipse is 0 0 Type an ordered pair ww The vertices of the ellipse are Use a comma to separate answers as needed Type an ordered pair using integers or fractions

Geometry

Heights & DistancesStep 1 Given information Player 1 and Player 2 are both equally likely to choose rock paper or scissors in a rock paper scissor game Step 2 a Let a b represent the outcome of the game where a and b are the choices of player 1 and player 2 respectively Let R represent the rock S represents the scissor and P represent the paper The total of 9 possible outcomes of the game will be PossibleA outcomes R R R P R S P R P P P S S R S P S S Each outcome is equally likely to happen with a probability of The probability model will be a b P a b Step 3 b From the above table there are only 3 outcomes player 1 is winning that are R S P R and S P The probability that Player 1 wins the game on the first throw will be computed as Winning outcomes Total outcomes R R 1 9 P Player 1 R P 1 9 R S 19 P R 1 9 P P 1 9 3 0 33 So the probability that Player 1 wins the game on the first throw is 0 33 P S 9 S R 1 9 S P 19 S S 10 9

Geometry

Heights & Distancesn 6 S 1 1 n 2 S 13 80 e Refer to the diagram for question 12 22 Plot a graph of the values of energy y axis against the square of the number of the level i e n on the x axis C

Geometry

Heights & DistancesFind the cosecant secant and cotangent of angle A given that a 17 3 and b 13 2 Although it is best to leave the ratios as reduced fractions for the purposes of this question round to 4 decimal places Diagram is for reference only and is not drawn to scale CSC A sec A cot A A C 000 B

Geometry

Heights & Distancesate a design sequence diagram of the Cancel booking use case according to the multilayered pattern Apply Jacobson Stereotypes in your diagram TE create the diagram using StarUML tool and save it as an image file Payment Reference Amount Cash payment sd Cancel Booking Ot Customer CustomerID Name Customer ContactNumber Address 1 Card Payment 1 select Booking 3 bk 4 Cancel bk 1 0 Figure 3 Domain Class Diagram of Hotel Management System User login 1 Hotel management system Room RoomNumber bedsNumber Floor 1 Hotel management system 0 Booking Booking ID Date from Date To Figure 2 System Sequence Diagram of cancel booking use case 2 DisplayBookinkDetails Ot

Geometry

Heights & DistancesSolution a n 100 SRS size The number of pupils who claimed they recycle is 55 We must decide whether there is persuasive evidence that more than half of the pupils at the school would indicate they recycle regularly using the Fathom dot plot which displays the results of taking 200 SRSs of 100 students from a population in which the genuine proportion who recycle is 0 50 A simulation is a model of random behaviour that is usually carried out with random numbers It is insufficient proof that more than half of the students at the school recycle because Yes was replied by 55 out of 100 pupils 55 100 0 55 We can see that the proportion of 0 55 has a lot of dots above it in the dot plot As a result a proportion of 0 55 is quite likely to be obtained when the genuine proportion is 0 5 and there is insufficient evidence to support the assertion that more than half of the school s students recycle b Because 63 out of 100 students answered Yes this statistic strongly suggests that the majority of the school s students recycle 0 63 63 100 We can see that the proportion of 0 63 has only one dot above it and no dots to the right of it in the supplied dot plot Thus while the genuine proportion is 0 5 a proportion of 0 63 is quite likely to be obtained and there is adequate evidence to support the assertion that more than half of the school s students recycle As a result the outcome

Geometry

Heights & Distances0 157 1 65 0 0108 0 0028 Z 0 157 1 65 0 0108 0 0028 1 1 solving for T The equation 1 is in quadratic form solving for by evaluating the roots of the quadratic equation Rewring the equatin 1 3 Solving for root Z 1 2 concentration Discarding the negative root 0 06 0 0 0556 0 05 0 04 0 03 0 02 0 82572 0 157 0 008 0 0 04315 0 01 ax bx c 0 T 0 root 0 root T 0 03 b b 4 a c 2 a 0 15 0 152 4 0 825 0 008 2 0 825 0 15 0 0225 0 0264 2 0 825 0 5 0 15 0 2211 2 0 825 1 0 4311 Distance Z 1 5 y 0 0128x 0 0557 R 0 9998 2 2 5

Geometry

Heights & DistancesDesign a relational schema and SQL quenes to iStore the basis functional dependencies i Check Fa functional dependency is part of the closure of besis set of functional dependencies stored in your relations designed above

Geometry

Heights & Distancesr 8 Give two other polar coordinate representations of the point one with r 0 and one with r 0 2 2 3 smaller r value r 0 Need Help Read It 2 X 0 larger r value 2 0

Geometry

Heights & DistancesA property is bing transported through a fluidat steady state trough a content cros sectional area at point the concentration is 278 x 10 amount of roperty m and 1 50 x 10 at point 2 t a distanceof 20 m away Thedificity depends on concentraion l as 8 0 150 1651 a calculate the teadystate fut if he two points were separated by 35 m but with he same concentrations How does the flux vary with the distance between the points Calculate the steady state fut if the concentration at point 2 was 150 x 10 amount of property using the right stance 20 to do the way with he diference in concentration b

Geometry

Heights & DistancesUse the diagram below showing the concrete floor of a building At a cost of 30 per cubic foot find the cost of having the floor poured Round your answer to two decimal places 50 ft 25 ft 6 in

Geometry

Heights & DistancesSolve Use 3 14 for Find the volume of the bushing shown below Round your answer to two decimal places 857 6 X in 6 in 8 in 16 in 24 in

Geometry

Heights & DistancesQuestion 9 Use the figure below to answer the following question B Given that AD and BC bisect each other at E which of the following justifies A ABE A DCE A SSS Postulate B C C D SAS Postulate Definition of Segment Bisector Definition of Congruent Triangles

Geometry

Heights & Distances1 Civil engineering is of immense importance because it plays a crucial role in designing constructing and maintaining the infrastructure that supports society From buildings bridges and roads to dams airports and water supply systems civil engineering ensures the safety functionality and sustainability of our physical environment It contributes to economic growth enhances quality of life and addresses societal needs such as transportation water re

Geometry

Heights & DistancesAs per the information given in the question Actual Budgeted Units 600 650 Flexible Budget We need to prepare flexible budget for the sales during the month of May In flexible budget rate will be standard rate or budgeted rate and units will be actual units sold So flexible budget Price per unit 800 780 Units 600 Price per unit 780 Actual Quantity 600 units Standard Quantity 650 units Actual price 800 Standard price 780 Sales price variance SQ AP SP Sales volume variance BP AQ BQ Explanation AQ Actual Quantity SQ Standard Quantity AP Actual Price SP Standard Price Sales price variance is positive so it s favorable Sales volume variance is negative so it s unfavorable Final Answer Total Sales C2 B2 B3 C3 Total Sales B2 C2

Geometry

Heights & DistancesDescription Common Shares Contibuted Surplus Recained Eamnings Cash Debit Earnings Per Share Revenue Debt to Equity Ratio 5 040 000 545 000 7 015 000 Credit 12 600 000 Place only one T in each row below indicating the impact of the share reacquisition journal entry on the following financial statement metrics Positive Negative Not No Impact Determinable

Geometry

Heights & Distancesa softball player named Jen You were d to find the probability of Jen getting at least 12 hits in her next 20 at bats when she has a batting average 40 Because we have the technology to find binomial probabilities and their sums quickly we could have Pix2121 1 Pix 11 1 0 53435 0 0565 where we fnd Ply 11 0 9435 by using the graphing ator tincion biomatf2004 or prestaly some other form of technology Suppose weddit het hat would be bound the 10565 answer quickly se the Normal Distribution as an approximation for the Binomial Distribution Find the mean and standard deviation of the binomial distribution where X8 20 0 4 Mean Standard Deviation b Using the mean and standard deviation fr a Normal Distribution find the z score that

Geometry

Heights & Distances8 In the problem below AABC AADC Solve for x Then use that value to find the length of BC 1 point B 12x 15 3x 30 BEAU 9 Can one of the triangle congruence theorem listed below be used to show the two triangles are congruent 1 point A Angle Side Angle Theorem OB Side Angle Side Theorem DC Side Side Side Theorem OD None of the theorems listed can be used to show congruence

Geometry

Heights & DistancesASSESSMENT Credit Checkpoint Complete the following problems Show all your work Triangles Part 1 Learning Goal from Lesson 4 1 4 4 I can prove the following theorems about lines and angles Vertical angles are congruent When a transversal crosses parallel lines alternate interior angles are congruent and corresponding angles are congruent Points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints 1 Use the figure to determine the value of x and y Lesson 4 1 1 point OA 25 and 21 are Complementary OB 25 and 21 are Supplementary C 23 and 24 form a Linear Pair Lingar Pair 5 2 Which of the following are true statements Select two that apply Lesson 4 1 1 point 2 3 How I Did Circle one ch I got it I m still learning it m x80

Geometry

Heights & Distancesfiber optic network to monitor power meters at residents homes The network is called Santa Joaquin Fiber Network SJFN Because SJFN had more capacity than was needed to monitor meters the city expanded its services to offer access to the network for city businesses The businesses use the network to communicate with each other and to access the Internet At the SJFN headend which is located with the city government offices three routers and WAN links connect to the Internet for use by the city The businesses on SJFN also use these routers to reach the Internet In addition to the business service SJFN also offers cable modem service to homes A cable modem router at the SJFN headend connects to the fiber optic network In the city neighborhoods hybrid fiber coax nodes bring coax cabling to each street and into the homes for cable modem Internet access The SJFN backbone consists of a fiber optic Gigabit Ethernet network that runs through the city in a ring topology The fiber optic ring connects the hybrid fiber coax nodes that bring coax cabling to each neighborhood Also connected to the ring are six data routers Each router links one or more Santa Joaquin businesses to SJFN via simple point to point connections At the business the fiber optic network enters the building and connects to a media converter A UTP cable connects to the media converter and typically to a 100 Mbps Ethernet switch The switch links the business s computers and servers in a star topology via UTP cabling Draw a network map that shows the topology of the SJFN and how the main mponents are connected