Geometry Questions

Solve for the value of a 529 8a 6

To find the distance across a river a surveyor chooses points A and B which are 197 ft apart on one side of the river see the figure She then chooses a reference point C on t opposite side of the river and finds that ZA 47 and LB 70 Approximate the distance from A to C A B 207 ft 208 ft 209 ft 206 ft A c ft Bo

Evaluate the sine cosine and tangent of the angle without using a calculator If an answer is undefined enter UNDEFINED 11 0 4 sin Cos 0 tan 8

Determine two coterminal angles one positive and one negative for each angle Give your answers in radians Enter your answers as comma separated lists 17 a 8 7 b 0 7 15 rad rad

Find the measure of the missing angles Answer Attempt 1 out of 2 g k O O 50 hl g m 39 kl h m O O

A television camera at ground level films the lift off of a space shuttle at a point 750 meters from the launch pad see figure Let 8 be the angle of elevation to the shuttle and let s be the height of the shuttle a Write 8 as a function of s 8 750 m Not drawn to scale b Find 8 when s 600 meters and s 1300 meters Round your answers to two decimal places s 600 meters 8 rad s 1300 meters 8 rad

Find the measure of the missing angle 65 a

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

Find the indicated side x if b 6 a 33 y 70 Use either the Law of Sines or the Law of Cosines as appropriate C O 5 164 A 22 369 14 527 3 354 a y X B

Find the measure of the missing angle a

A 16 ft ladder is leaning against a building If the base of the ladder is 6 ft from the base of the building what is the angle of elevation of the ladder Round your answer to one decima place O ICE AN How high does the ladder reach on the building Round your answer to the nearest whole number ft

In the triangle below with right angle D suppose that m B 3x 26 and mz C 5x 16 Find the degree measure of each angle in the triangle C D k 5x 16 3x 26 B mL B m2 C m2D O 0

A 18 ft ladder is leaning against a building If the base of the ladder is 6 ft from the base of the building what is the angle of elevation of the ladder Round your answer to one decimal plac 0 How high does the ladder reach on the building Round your answer to the nearest whole number ft

2 ounces of pure gold was 2 640 Complete the double number line to show the cost for 1 3 and 4 ounces of gold 0 2 640 cost in dollars 6 600

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

Find the scale factor from the following similar figures 8 4 cm 28 cm Original 35 cm New 11 CH

Which of the following best describes the dilation Figure 1 Figure Il Figure III Figure IV

13 15 7x 10 10x 3x 85 A 8x 5 A 14 A 16 48 5x 2 134 11x 5 9x 3 A 6x

Solve for x 5 7 30 66 x x 44 55 2 201 8 60 30x 10 5x 40

Find the measure of angle A 9 Fa 71x 1 11 0 x 51 20x x 61 80 A 28 28 10 A 12 x 34 otsib olgua does lo ozess x 64 x 52 75 67 x

Find the measure of each angle indicated 1 55 70 3 80 7 39 DAY 2 4 35 85 85 35

The function G x 0 01x x 63 models the wage gap as a percent x years after 1980 in Country A The graph of function G is shown underneath the actual data a Find and interpret G 10 Identify this information as a point on the graph of the function G 10 in the year in country A Type whole numbers earnings were 8 Median Women s Earnings as a Percentage of Median Men s Earnings in Country A 87 Wage Gap percent 95 90 85 90 80 75 70 65 50 45 63 74 79 1980 1990 2000 2010 The Graph of a Function Modeling the Data

2 In the figure to the right QR 45 feet and RS 15 feet Find QS

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

the figure to the right EG 12 EF 2x 3 and FG x 6 Find EF and FG EQ F 2r 3 x 6

1 In the figure to the right PR 12 inches and QR 4 inches Find PQ HR a PR 1

Use the figure below to find the exact values of the half angles 5 Find sin cos and tan sin cos tan 11 12 0

STATE The toco toucan Ramphastos toco is the largest member of the toucan family and possesses the largest beak relative to body size of all birds This exaggerated feature has been interpreted in various ways such as being a refined adaptation for feeding However the large surface area may also be an important mechanism for radiating heat and hence cooling the bird as outdoor temperature increases Here are data for beak heat loss as a percent of total body heat loss at various temperatures in degrees Celsius Temperature C 15 16 17 18 19 20 21 22 Percent heat loss 32 34 35 33 37 46 55 51 from beak Temperature C 23 24 25 26 27 28 29 30 Percent heat loss from beak 43 52 45 53 58 60 62 62 access the complete data set click the link for your referred software format cel Minitab14 18 Minitab18 JMP SPSS TI R Mac KT PC TXT CSV Crunchlt rom a graph in G J Tattersall et al Heat exchange from the toucan bill als a controllable vascular thermal radiator Science 325 2009 pp 470 O Macmillan Learning PLAN Plan to create a scatterplot and compute a numerical correlation metric to analyze the relationship between percent heat loss from beak response variable and temperature explanatory variable SOLVE Use software of your choice to create a scatterplot of percent heat loss from beak versus temperature Examine the scatterplot and describe the pattern Identify the correct interpretation of the relationship between temperature and percent heat loss based on the scatterplot r There is a weak negative linear relationship between temperature and heat loss There is a strong positive linear relationship between temperature and heat loss There is a moderately strong positive nonlinear relationship between temperature and heat loss O There is a weak negative linear relationship between temperature and heat loss Calculate the correlation r between temperature and the percent of heat loss from beak Provide your answer with precision to three decimal places

Use the figure below to answer items 15 through 17 given that A B C D 8 points each P P1 B4 D4 A4 C4 T B Du C P3 P2 B2 1 T 2 K B3 L4 D3 C3 16 C4 B4 D4 A4 P3 P2 CA D4 17 A4 D4 C4 B4

17 Mia has 80 m of fencing material and would like to fence a rectangular plot o Determine the a dimensions of the plot that would ensure maximum area b maximum area that can be enclosed with 80 m of fencing material c the domain and range for the area function

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

1 Pin 2n Zn 26 A 29 4 5 1 0 13 13 23 21 2 25 1 3CH 28 26 F v T 27 a v COS sin 12 i 2 iv 0 v 6 cot 14 d iv g viii and 35 D 39 B 43 D 11 21m viii 6 and 0 ix a circle ii F vi T b i e ii b vii 29 No 33 27 B 30 False 2x 3 NIO EXEMPLAR PROBLEMS MATHEMATICS 36 C 40 A 44 D 2 P n 1 2 3 28 A 5 3EXERCISE NIM Fa 3 0 2 30 15 vi vii 0 x 2 3 21 i T vii F c 1 vi 4a 1 37 B 41 A 45 B 34 Real axis 38 A 42 B 31 2 3 21 46 2 B iv T vii F be repubished hed

This question 1 point s possible Sketch an angle 8 in standard position such that has the least possible positive measure and the point 3 3 is on the terminal side of 0 Then find the values of the six trigonometric functio for the angle Rationalize denominators if applicable Do not use a calculator Choose the correct graph below OA B Select the correct choice below and if necessary fill in the answer box to complete your choice O C O D Submit quiz

O A 18 Sketch an angle 0 in standard position such that has the least possible positive measure and the point 6 8 is on the terminal side of 0 Then find the exact values of the six trigonometric functions for 0 p 18 18 9 X 18 A o OB 18 Ay 18 9 9 18 X 18 nus pos This question 1 point s possible Select the correct choice below and if necessary fill in the answer box to complete your choice O C possible 18 9 18 Ay 19 19 W 18 18 Submit quiz 5

The terminal side of an angle 8 in standard position passes through the point 2 1 Use the figure to find the following value cos e cos 8 Type an exact answer in simplified form Rationalize all denominators

Lines m and n are parallel and are intersected by transversal line 1 1 5 E m 2 6 3 4 8 7 If the m 1 71 what is the measure of its corresponding angle Type the correct answer in the box Use numerals instead of words For help see this worked examp

Consider two displacement vectors defined by their magnitudes and directions as follows A has a magnitude of 37 0 m and is directed in the direction B has a magnitude of 52 0 m and is directed 33 0 clockwise from the direction Let C A B What is the direction of C Note Express your answer as an angle

You will explore the relationships between corresponding angles when two parallel lines are cut by a transversal Directions Read the instructions for this self checked activity Type in your response to each question and check your answers At the end of the activity write a brief evaluation of your work Activity In this activity you will use the GeoGebra geometry tool to explore the relationships between the corresponding angles formed when a transversal cuts two parallel lines Open parallel lines and transversals and complete each part of the activity For help watch this video about using measurement tools in GeoGebra Part A Measure and record all eight angles formed between the transversal line EF and the parallel lines AB H and CD Take a screenshot of your diagram showing the measures of all the angles and paste it in the space below BIUX X 15px AVV EEEEEE HY

he figure to the right shows the feasible set of a transportation problem and the straight line of all ombinations of shipments for which the transportation cost is 108 Complete parts a through c elow D feasible set a The objective function is cost 288 3x 2y Give the linear equation in slope intercept form of the line of constant cost c 3 Simplify your answer Do not factor Use integers or fractions for any numbers in the equation A C B y x 0 Q

the triangle below LF is a right angle Suppose that mz E 5x 16 and mz G 4x 20 G F 4x 20 45x 16 E a Write an equation to find x Make sure you use an sign in your answer Equation b Find the degree measure of each angle mLE 0 mLF m G 0 0 X X S

m the triangle below suppose that m 2 V 2x 9 mz W 7x 1 and m2 X x ind the degree measure of each angle in the triangle 2x 9 W 7x 1 X m V m2 W mLX 0 0 0 O X

Note In case the lines L and L do not pass through the origin we may take lines L and L which are parallel to L and L respectively and pass through the origin If instead of direction ratios for the lines L and L direction cosines namely 1 m n for L and l m n for L are given then 1 and 2 takes the following form cos 0 1 mm nn as m 1 m n and sin 0 1 m 1 m m n m n n 1 1 4 Two lines with direction ratios a b c and a b c are i perpendicular i e if 0 90 by 1 ii parallel i e if 0 0 by 2 a a by C Now we find the angle between two lines when t acute the angle between the lines then aa bb ce 0 F a Ab and F b b b B In Cartesian form if 0 is the angle between the lines 3 3 2 2 b cos8 4 not to cos 8 19 T M cos 8 9 56 3 4 12 19 3x7 21 X X y 2 2 and a by where a b c und a b c are the direction ratios of the lines 1 and 2 respectively then Example 7 Find the angle between the pair of lines given by F 3i 2 4k M 2 2k aa bb cc b b c Rationalised 2023 24 and 7 57 2j 37 2j 6k Solution Here 7 23 2k and h 3i 2 6k The angle 8 between the two lines is given by bb 2 2k 37 27 6k THREE DIMENSIONAL GEOMETRY equations are given If 0 is 1 4 4 9 4 36 3 Hence 0 cos Example 8 Find the angle between the pair of lines x 3 y 1 2 3 published 4 ched 1 2 385

E The diagram shows a vertical pole PQ which is supported by two wires fixed to the horizontal ground at A and B Find a b BQ 40 m PBQ 36 BAQ 70 ABQ 30 the height of the pole PQ the distance between A and B 70 A 360 og 300 B

In the triangle XYZ XY 14 cm XZ 17 cm and angle YXZ 25 A is the foot of the perpendicular from Y to XZ Calculate a the length XA b the length YA c the angle ZYA

Use the diagram to the right If AD 16 and AC 2y 2 find the value of y Then find AC and DC What is the value of y y Type an integer or a decimal Find AC and DC Type an integer or a decimal DC Type an integer or a decimal AC A E D B C

6 Complete the statement that best describes the intercept of your graph when the quantity The value of the quantity zero Please select a valid drop area is value unit is

ne time increases 1 s for every 1 cm of speed moices Reset S 0 time 27705 6277 cm position Submit Answer X unlimited submissions remaining speed

23 Pentagon PENTA with PE EN 24 Hexagon NGAXEH with LHEX LEXA

20 A ray that divides the angle into two angles is the angle bisector 21 An obtuse triangle has exactly one angle whose measure is greater than 90 biosoqsil 22 Suppose a set of thin rods is glued together into a triangle as shown How would you place the triangular arrangement of rods onto the edge of a ruler so that they balance Explain why