Heights & Distances Questions and Answers

6 What if a restaurant needed to build a wheelchair ramp for its customers The angle of elevation for a ramp is recommended to be 5 degrees If the vertical distance from the sidewalk to the front door is 2 feet what is the horizontal distance that the ramp will take up x How long will the ramp be z Round your answers to the nearest hundredth 3 points z 2 09ft x 61ft

For Exercises 2 6 match the term on the left with its figure on the right 2 Trapezoid 3 Rhombus 4 Rectangle 5 Kite 6 Parallelogram E B F For Exercises 7 10 sketch and label the figure Mar 4 D

The sun is 18 above the horizon Find the length of a shadow cast by a park statue that is 12 feet tall Round your answer to one decimal place ft

10 The contractor you are working for needs to know the height of a building to see if his 300 foot crane will reach the top If you read an angle of inclination of 40 13 52 at a distance of 350 ft from the base of the building what is the building height and will the crane reach the top Draw a neat diagram

Follow the instructions for each problem Figures shown are NOT drawn to scale 1 If AB 48 and BC 22 then AC 2 3 5 7 9 11 A JL 84 If JK 5x 8 and KL 4x 4 then x FG 8x 4 If GH 4x 8 and FH 15x9 then FG F S B T is the midpoint of SU If ST 16 then SU A G If AB 18 and AC 3x 6 then x B Green 39 H If DE 7x 3 and EF 9x 19 then EF 4 Purple 60 6 8 If DF 51 and EF 32 then DE 12 D R RT 60 If RS 2x 1 and ST 4x 7 then x P PQ 2x 3 If QR 5x 7 and PR 10x 11 then PR E S 10 If TU x 7 and UV 5x 13 then UV T D is the midpoint of CE If CE 28 then DE Match the question number with the answer below Color the picture accordingly Blue 57 Orange 12 Orange 19 Green 8 F R If QR 8x 1 and QS 20x 26 then RS R E Blue 32 Yellow 10

31 Find h as indicated in the figure 29 5 392 ft H 49 2 h WAL

35 Height of an Antenna A scanner antenna is on top of the center of a house The angle of elevation from a point 28 0 m from the center of the house to the top of the antenna is 27 10 and the angle of elevation to the bottom of the antenna is 18 10 Find the height of the antenna

A national automobile association determines that the mean fuel consumption for vehicles in a particular state is 23 6 miles per gallon with a standard deviation of 5 8 miles per gallon If a Normal model is applicable approximately what percent of vehicles in that state should get between 28 and 30 9 miles per gallon Use a calculator or a Normal distribution table to help calculate your answer to the nearest tenth of a percent A 10 4 B 12 0 C 30 9 D 22 4

C 21 3 X 66 4 y

1 Determine the length of the unknown sides for each of the right angled triangles below b 10 2 9 cm 61 2 Z I Z y 34

different regions in 1985 and in 2005 Population in Population 1985 in 2005 4 9 10 6 4 109 1 1 x 10 1 3 x 109 7 6 x 108 1 1 109 2 4 108 3 0 108 8 9 x 106 7 2 x 106 Place Entire world China India United States Bulgaria a Determine the ratio of the population of the entire world to that of China in 2005 giving your answer to the nearest integer b Find the increase in the world s population between 1985 and 2005 c Calculate the percentage change in the population of each of the four countries giving your answers accurate to 3 sf List the countries according to their percentage change from highest to lowest d State whether or not you agree that it

The endpoints of two segments are given Find the length of each segment If necessary round your answers to the nearest tenth EF E 1 1 F5 1 and GH G 3 1 H 1 6 The length of EF is Tell whether the segments congruent 24 Yes 25 O No If they are not congruent tell which segment is longer The length of GH is about O EF is longer GH is longer O EF and GH are congruent The coordinates of the midpoint of GH are Ms 0 and the coordinates of one endpoint are H 2 9 The coordinates of the other endpoint are Find the distance between the points C 6 5 and D 3 1

In the right triangle find the length of the side not given Give an exact answer and an approximation to three decimal places 4 a 6 c 10 a The exact value of b is Type an exact answer using radicals as needed www

Choose the best selection for the quadrilateral with vertices at the following points 1 0 5 0 1 3 5 4 Hint Start by graphing the points Distance Formula d x2 x y2 y A Parallelogram B Trapezoid C Rhombus D Rectangle

e viewing angle 0 of an object is the angle the object forms at the lens of the viewer s eye The viewing angle is related to the object s height H and distance from the viewer D through the formula tan 2D A forest ranger views a tree that is 160 feet away with a vie gle of 18 How tall is the tree e height of the tree is approximately feet

Use a reference angle to write sec 25 in terms of the secant of a positive acute angle in radians 36

25 If the circumference of the following circle is 10 II inches find the perimeter of the square inches

Question 31 Find the midpoint of the line segment joining the points 1 2 and 1 2 O 0 0 Points 2 O 1 2 O 1 2 O 2 1

12 Check to see if the sides are proportional by creating ratios between corresponding sides and reducing the fractions Shortest Sides 5 Middle Sides Longest Sides 13 13 Are the two triangles gimilar Similar

The length of a rectangle is 8 inches more than its width Set up an equation to find the width of the rectangle if the area is 32 sq inches Owx 8 32 Ow 8 w 32 Ow 8 w 32 w 8 w 32

wide is it O 2 ft O 1 ft O 3 ft O 4 ft ectangular mat is 16 feet It is 6 feet long How

Question 2 Points 3 A 42 inch wire is bent into the shape of a rectangle whose width is twice its length Set up an equation to find the length of the rectangle O 2 21 1 42 O 21 1 42 O 21 1 2 42 O 21 1 42

Identify the geometrical name of the object shown below By lidar Sagdejev Spedious GFDL http www gnu org copyleft id html or CC BY SA 4 0 https creativecommons org licenses by sa 4 0 from Wikimedia Commons Rectangular prism O Triangular prism Hexagonal prism

All changes a Two buildings building A and building B are 200 and 1000 feet tall respectively The two building are placed side by side and a telephone wire is connected from the top of building A to the top of building B creating a 20 a from building B to building A Building A is on the left and building B is on the right 12 What is the difference in the heights of the two buildings Height Difference feet 13 We want to know how far apart the buildings are Which trigonometric ratio could we use with the given information to find the missing distance 14 Find the distance between the two buildings 20

15 40 B 75 ft Ashley you are standing 75 ft away from the base of a tree and using your awesome powers of deduction and the proper geometric tools you ve figured out that the angle of elevation from the ground to the 40 4 Describe the process that you d go through to solve for the height of the tree using the given information i U Font Family AA A FEE EB

5 These are 6 Find x and y Y 213 150

Problem 60 Let f x y 4 y to answer the following A Explain why the cross section for the surface z f x y produced by cutting it with planes parallel to x 0 are semicircles of radius 2 B Describe the cross sections of the surface in the planes y 0 y 2 and y 3 C Describe the surface z f x y

4 Find the area of the shaded region The units are in meters A 6 TM

5 Rectangle A is dilated to form rectangle B A 6 e 20 B 30 Target due 10 31 23 39 5 75 What scale factor was used Enter the answer and also provide a 1 sentence explanation that describes how you determined your answer Review the rub you will be evaluated

EXTRA CREDIT The units are in yards Find the area of the shaded region Ashaded Region Tyd

10 The volume of the right rectangular prism is V 270 cm Write a quadratic equation in terms of x Don t solve the equation 2 points x 3

9 A lot for sale in a subdivision has the shape of the quadrilateral shown in the figure Find the area the lot rounded to two decimals 10 points 75 ft 800 40 ft 135f 128 ft

A ball is thrown from an initial height of 4 feet with an initial upward velocity of 40ft s the ball s height in feet after seconds is given by the following Find all t values of for which the ball s height is 26 feet

he what you w ciple Part II 19 Points 1 A e radius of a circle is 5 mm then find the area of the Posttest O 5 square mm O 10 square mm O 15 square mm O 25 square mm Complete

Match the equation with the sentence Susanne was hiking down from Mt Whitney She started at 14 500 ft above sea level and descended 375 ft every 30min Kirk was hiking up to Mt Whitney He started at 7545 ft above sea level and ascended to the top 14500 ft after about 8 5 hours of hiking Using an average pace choose the function that describes his elevation relative to the time in hours Jolie was hiking up to Mt Whitney She started at 7545 ft above sea level and ascended to the top 14500 ft after about 10 hours of hiking Using an average pace choose the function that describes her elevation relative to the time in hours Juan was hiking down from Mt Whitney He started at 14 500 ft above sea level and descended 1400 ft every hour Choose Choose E t 70 3 t 14500 E t 818 81 7545 E t 6961 7545 E t 75 6 t 14500 Choose Pedro loves to try new adventures His most recent adventure was jumping out of an airplane His special watch tells him his altitude He set a timer at the moment he opened

Tutorial Exercise The Cartesian coordinates of a point are given a 7 7 1 Find polar coordinates r 8 of the point where r 0 and 0 0 2 ii Find polar coordinates r 8 of the point where r 0 and 0 0 2 b 5 5 3 i Find polar coordinates r e of the point where r 0 and 0 0 2 ii Find polar coordinates r e of the point where r 0 and 0 0 2

Solve the equations for solutions in the interval 0 360 Use a calculator for Problem 12 give the answer to the nearest hundredth of a degree 9 Sin x 1 3 10 Sec x 2Sec x 0 11 2cos x root 3 0 In degrees just verifying I am doing this correctly Trigonc Sub subj Sear

Use fundamental identities to find the values of the trigonometric functions for the given condition sec 0 6 and tan 0 0 sin 0 cos 0 tan 0 cote sec 0 CSC 0

Question 6 Find the distance between A and B 6 4 2 Points 2 20 Y 18 16 14 12 10 8 6 4 2 0 4 5 O 5 units O 6 units O 7 units 8 units 2 A 4 4 6 8 B 10 12 14 16 18 20 X

Question 10 Points 2 Write the equation of a line that is perpendicular to y 4 5 x 2 and has a y intercept of 1 O y 5 4 x 1 O y 5 4 x 1 O y 4 5x 1 O y 4 5x 1

Find the equation of a line parallel to 2x 3y 9 that passes through the point 1 3 O 2x 3y 11 O 2x 3y 11 O 3x 2y 11 3x 2y 11

Write an equation of a line that is parallel to y 2x 1 and passes through the point 4 6 O y 2x 2 Oy 2x 2 Oy 2x 4 Oy 2x 4

The table below shows the distribution of FTC complaints categorized by payment method and the dollar value of all transactions made under each method Method of payment Bank Account Debit Cash Advance B 0 16 C 0 30 Check Credit Cards Internet Money Order Prepaid Cards Telephone Bill Wire Transfer Total Number of complaints Total value of transactions 85 433 040 168 972 138 88 603 695 96 440 695 9 651 081 38 527 17 332 12 917 46 736 5 734 8 707 119 100 1 028 106 472 356 553 55 898 113 80 860 327 870 511 500 705 082 1 087 434 682 If an FTC complaint is chosen at random which of the following is closest to the probability that the complaint is related to the payment method whose transactions accounted for the highest dollar value A 0 05

A two sample test for means was conducted to determine if the completion time for continuing education programs for nurses differed when costs are paid by employers Yes versus when individuals paid out of their own funds No The Excel Data Analysis tool results are provided Complete parts a through c below Click the icon to view the Excel Data Analysis tool results Therefore fail to reject the null hypothesis The data do not provide sufficient evidence to conclude that t b Explain how to use this information to draw a conclusion if the null hypothesis is Hy 20 Clearly s The alternative hypothesis is H HY HN 0 The critical value is 1 746 The p value is 0 737 Type an integer or a decimal rounded to three decimal places as needed Therefore fail to reject the null hypothesis The data do not provide sufficient evidence to conclude that t c Explain how to use this information to draw a conclusion if the null hypothesis is Ho y N 0 Clearly s ly Ho The alterna The critical The p value Type an in Thoroforn reject fail to reject ded to three decimal places as needed sothoric The data Excel Data Analysis tool results tTest Two Sample Assuming Unequal Variances Yes 33 987 447 847 12 Mean Variance Observations Hypothesized Mean Difference df t Stat P TST one tail t Critical one tail P TS1 two tail t Critical two tail provede suffrent evidence to conclude that the mean completion time is Print D 16 0647 0 263 1 746 0527 2120 Done No 28 153 352 156 8 for nurses when costs are paid by empowers

14 An observer in the top of a lighthouse determines that the angles of depression to two sailboats directly in line with the lighthouse are 3 5 and 5 75 If the observer is 125 feet above sea level find the distance between the two boats Show your main steps 5 points y 3 5 X 5 75 125 f 25 f

32 10 X Solve for x Round to the nearest tenth

In Exercises 5 to 22 find the missing lengths Give your answers in both simplest radical form and as approximations correct to two decimal places X N Exercises 5 8 7 Given Find Right AXYZ with XZ YZ and XY 10V 2 Y7 and Y7

A two sample test for means was conducted to determine if the completion time for continuing education programs for nurses differed when costs are paid by employers Yes versus when individuals paid out of their own funds No The Excel Data Analysis tool results are provided Complete parts a through c below Click the icon to view the Excel Data Analysis tool results a Explain how to use this information to draw a conclusion if the null hypothesis is Ho Hy HN 0 Clearly state the correct critical value and p value and your conclusion The alternative hypothesis is H Hy HN 0 The critical value is 1 746 ww The p value is 0 263 Type an integer or a decimal rounded to three decimal places as needed Therefore fail to reject the null hypothesis The data do not provide sufficient evidence to conclude that the mean completion time is longer for nurses when costs are paid by employers b Explain how to use this information to draw a conclusion if the null hypothesis is Ho Hy HN 20 Cle The alternative hypothesis is H Hy HN 0 The critical value is 1 746 h The p value is Type an integer or a decimal rounded to three decimal places as needed Excel Data Analysis tool results t Test Two Sample Assuming Unequal Variances Yes 33 987 Mean Variance Observations Hypothesized Mean Difference df t Stat 447 847 12 0 16 0647 No 28 153 352 156 8 X

Find the surface area obtained by rotating 1 x 2 1 x 1 about the x axis

The accompanying data gives the results of a survey on the number of hours spent online per week on a certain social networking website Determine if the mean number of hours spent online per week is the same for males as it is for females Assume that the population variances are unequal Click the icon to view the social media survey data Is there sufficient evidence at the 0 05 level of significance that the mean number of hours spent online per week is the same for males as it is for females Determine the null hypothesis Ho and the alternative hypothesis H Let females be population 1 and males be population 2 Ho H Type integers or decimals Do not round b 2 Female 3 Female 4 Female 5 Female 6 Female 7 Female 8 Female 9 Female 10 Female 11 Female 12 Female 13 Female 14 Female 15 Female 16 Female 17 Female 18 Female 19 Female 20 Female 21 Female 22 23 Gender 4 Male 9 Male 8 Male 5 Male 7 Male 12 Male 1 Male 6 Male 2 Male 5 Male 8 Male 13 3 7 3 8 5 Male 4 Male 6 8 Hours online week 6 14 6 4 6 4 9 3 7 8 6 4 4