Geometry Questions

Question 9 Let right triangle ACB have C 90 and let sides a b and c be opposite angles A B and C respectively If a 15 and b 8 find c Answer exactly C

16 in Fig P5 8 1 20 in r 38 in

se an identity to simplify the following expression tan 17 1 tan 17 Choose the correct expression equal to OA 1 2 cos 17 OC 1 2 tan 34 tan 17 1 tan 17 below B 1 TIN tan 17 OD sin 34 G

Determine the magnitude and direction of the vertical shift and the phase shift for the function below f x sin x 7 3 Select the correct answer below O O O The vertical shift is left 7n units down and the phase shift is 3 units to the 4 The vertical shift is 7 units up and the phase shift is 3 units to the left 4 7 The vertical shift is 3 units up and the phase shift is right The vertical shift is right 7 The vertical shift is 3 units down and the phase shift is left 4 7n 4 units to the units up and the phase shift is 3 units to the 4 7x O The vertical shift is 3 units down and the phase shift is right 4 units to the units to the 11

s Show 12 35 using an area region model

Find all solutions if 0 0 360 Separate your answers with commas and do not degree symbols sin 30 0 3 2

0 NUMMMM 1 2 5 2 1 0 0 Ay 1 T 10 47 5 2 y sin x X n 5 Q G 5 3 2 1 0 0 Ay I 0 1 2 3 2 Drag each graph above to match the function below y sin x n x X T 5 1 0 0 V 6 5 15 5 y cos x GLOB T 5 y cos x 5 3 2 1 0 0 2 0 6 11x 5 Q

Given ZA ZEBC and AB BC Prove BE AC Note quadrilateral properties are not permitted in this proof Step 1 try Statement ZA ZEBC AB BC Type of Statement Reason Given B D E

In Exercises 47 54 use the figures to find the exact value of each trigonometric function 3 5 8 0 C 7

4 y x 5 y x 5 PART A Graph the functions Q

V and w head to tail as needed to sketch the indicated vectors a u v b u v w C U V d u w Choose the correct sketch for u v O A Q Choose the correct sketch for u v W O A Choose the correct sketch for u v O A Q O B B OB Q Q C C O C O C u Q G 5 W O D O D O D Q Q G Q

66 Given Segment TX is an angle bisector of Triangle NT Segment TX is the altitude of Triangle NTL Prove Angle NTX is congruent to Angle LTX

2 5 pts Two cables are attached to a tower to stabilize it In the figure the cable on the left is 150 ft long and forms an angle of elevation of 58 The cable on the right forms an angle of elevation of 29 How long is that cable marked with an x Show your work Round to 1 decimal Use correct units 150 ft 58 Tower X 29

Write a coordinate rule for the composition the blue preimage to the green image P L 2 6 Ay M S R 2 4 K 6 x

Simplify the following expression as much as possible tan cot x tan x O tan x cot x 9T 2 X

Find all solutions of the following equation sec x 4 0 Select the correct answer where k is any integer 5TT 3 TU 3 TL 3 TC 3 TU 3 KIT 2k KI 2k 2 3 2 T 3 2 3 KI 2k KT 4 3 2k 4T 3 5TL 2k 2k 3 ki 5TT 3 k

Find the values of the trigonometric functions of t if cos t 3 and the terminal point of t is in quadrant III 5 sin t O sin t 4 5 sin t cos t 4 5 4 5 3 5 3 BR tan t E 5 cos t cos t EL 4 tan t cot t 3 3 5 tan t 4 3 4 cot t 4 3 cot t 3 4 3 4

Find the perimeter of the following figure with the indicated dimensions Use 3 14 Round your answer to the nearest hundredth if necessary 3 67 ft 1 62 ft 7

The graph shows how the path of a stream of water changes when the hose is held at two different angles Scale 1 unit 1 f Nozzle beld at 60 angle Nozzle held at 30 angle 6 5 4 3 2 1 1 2 3 4 5 6 7 a At which angle does the stream of water shoot up higher 60 How much higher X ft b At which angle does the stream of water shoot out farther 30 How much farther x ft

In 17 18 Find the value then find the measure of each angle 17 7x 12 R 101 12 T 3x 28 S 18 In 19 Use a two column proof to find the value of the variable Justify each statement 19 m RST 10x 12 and m USV 32 x 32 X 3x 75 Statement m RST 10x 12 and m USV 32 x Reason Given

Roll the Die C X Let s implement your randomization plan Roll the die below and assign treatments to each of the nine cows shown in the picture below by marking or circling each cow eyes marking place a circle around the cow crosses marking place an X over the cow no marking underline the cow Below is the randomization plan you proposed on the previous screen You can go back and make changes to your plan if you need To use a 6 sided die to randomly assign each cow in a herd of 50 cows to one of three treatments artificial eyespots cross marked or unmarked you can follow these steps 1 Label the die Assign two faces e g 1 and 2 for the artificial eyespots treatment Assign two faces e g 3 and 4 for the cross marked treatment Assign two faces e g 5 and 6 for the unmarked treatment 2 Roll the die for each cow in the herd By following this labeling

Find the exterior angles of the double triangle 30

In 16 Use a two column proof to find the value of the variable Justify each statement 16 m VST 11x and m RST 50 x R T S U Statement m VST 11x and m RST 50 x Reason Given

In 14 15 Find the value of the variable then find the measure of each angle 14 15 15x2 9x 10 154 3x 7

Question Answer Angst of s Watch Video From the observation deck of a skyscraper Bentley measures a 48 angle of depression to a ship in the harbor below If the observation deck is 969 feet high what is the horizontal distance from the base of the skyscraper out to the ship Round your answer to the nearest tenth of a foot if necessary Submit Answer Show Examples G

Question Watch Video Answer Attempt 1 out of 2 Show Examples From a hot air balloon Ian measures a 30 angle of depression to a landmark that s 1250 feet away measuring horizontally What s the balloon s vertical distance above the ground Round your answer to the nearest tenth of a foot if necessary G

Question Watch Video Answer Attempt 1 out of 2 Show Examples From a hot air balloon Adriel measures a 22 angle of depression to a landmark that s 743 feet away measuring horizontally What s the balloon s vertical distance above the ground Round your answer to the nearest hundredth of a foot if necessary

Question Answer Attempt 1 out of 2 Watch Video Mamadou leans a 18 foot ladder against a wall so that it forms an angle of 75 with the ground What s the horizontal distance between the base of the ladder and the bottom of the wall Round your answer to the nearest tenth of a foot if necessary foot Show Examples

uestion Watch Video Answer Attempt 1 out of 2 Show Example he angle of elevation to a nearby tree from a point on the ground is measured to be 74 How tall is the tree if the point on the groun 4 feet from the bottom of the tree Round your answer to the nearest tenth of a foot if necessary

Question A boat is heading towards a lighthouse whose beacon light is 113 feet above the water The boat s crew measures the angle of elevation to the beacon 11 What is the ship s horizontal distance from the lighthouse and the shore Round your answer to the nearest tenth of a foot if necessary Answer Attempt 1 out of 2 Watch Video Show Examples

Question Solve for 2 Round to the nearest tenth if necessary x 1 94 72 J

uestion Express tan K as a fraction in simplest terms L 47 M 17 K

4 Suppose a large population has an unknown mean and a known standard deviation 0 4 4 How many individuals should be randomly sampled from this population so that the sample mean is within 0 75 unit of with 95 confidence Answer Previous Answer 133 Q Search Return to overview H hp Jy

Given a stained glass window with 1 29 inches and d portion of the window Note Not to scale Area 1 d 85 1 d square inches 55 inches find the area of the stained glasse

Use the traditional method to test the given hypothesis At the a 0 05 significance level test the claim that a population has a standard deviation of 20 3 A random sample of 18 people yields a standard deviation of 27 1 O There is not sufficient evidence to warrant rejection of the claim that the standard deviation of the population is equal to 20 3 O There is sufficient evidence equal to 20 3 support claim that the standard deviation of the population is O There is sufficient evidence to warrant rejection of the claim that the standard deviation of the population is equal to 20 3 O There is not sufficient evidence to support the claim that the standard deviation of the population is equal to 30 3

the perimeter add each side 2 Find the area of a circle 3 Find the volume of the L x W x H

Find the measure of the indicated angle 1 A This is the only question in this section Question Find m A Answer Attempt 1 out of 2 A

A pyramid was built about 2590 BC Its original height was 518 feet 11 inches but due to loss of its topmost stones it is now shorter Find the current height of the pyramid using the information given in the figure on the right The current height of the pyramid is feet CHCEC 38 8 45 52 the final newer Thed to two decimal places as needed

For problems 1 and 2 let z y be a point on the unit circle with the corresponding angle 0 2 7 1 Use the given information to find tan 8 5 points cos 8 0

2 Let 0 6 a Find y 5 points b Sketch the unit circle and on it indicate the point z y as well

3 A cosine function has the given properties Amplitude 3 phase shift a Write the function in the form y Acos z d where A 0 3 points b What is the domain of the function 3 points c What is the range of the function Use interval notation 3 points d Sketch one period of the graph starting at z 0 Clearly label each intercept and other key points such as max and mins 2

7 In 5 8 Find the value of the variable then find the measure of each angle 5 1 4z 10 32 10y 52 6 8 4x 1 7x 3 7 9x 4 113

Statement ZMON 4x 17 and m2QOP 67 Reason Given

In 1 3 Use the given figure and write a two column proof to find the value of the variable justify each step 1 NIH 10x 5and m2MJK 3x 30 Reason Given Statement m NJH 10x 5 and m MJK 3x 30

N 2 mZMON 4x 17 and mZQOP 67 M M 3 m AEC 23x 83 and m DEB 5 12x 5z 9 D E K B In 4 5 Find the value of the variable then find the measure of each angle 4 8z Statement mZMON 4x 17 and m QOP 67 Statement mZAEC 23x 83 and mZDEB 5 12x 5 4x 1 65 Reason Given Reason Given

3 1 LA20 Er 1 TRIGONOMETRIC RATIOS USING SIN COS AND TAN In 4 6 find sin R cos R tanR Write each answer as a fraction and as a decimal rounded to three decimal places 4 R 6 T 30 T 15 sin R cos R n R 25 2 S 5 S sin R cos R opposite A for adjacent or H for hypotenuse from the indicated angle 3 tan R 24 26 10 R 16 S sin R cos R 34 A

The figure shown is a rhombus HJ has length 6 FG has length 10 Find the length of FJ E H 6 J I

8 Graph the equations below to form the figure Label the coordinates of the vertices 1 y x 2 y 3x 9 3 y 2 x 4 y 5 10 10 5 10 4 points 10 4 points

3 Points A 5 3 and B 7 6 lie on AB Points C 7 6 and D 1 10 lie on CD Which statement is true a AB CD b AB 1 CD C AB CD are the same line d AB CD intersect but are not perpendicular Using the same information from the problem above which statement is true about the length of the segments a AB CD b AB CD c AB CD d Not enough information is given

7 Graph the equations below to form the figure Label the coordinates of the vertices 10 3 y 4 2 3 y 2 x 1 y 1 x 4 x 5y 10 10 4 points a How many sets of parallel sides does the figure have Show calculations to justify your answer 4 points b How many right angles does the figure have Show calculations to justify your answer 1 point c Does the figure have 4 congruent sides Show calculations to justify your answer d What is the most precise name for this figure 4 points 2 points