Name ______Date ______
Geometry Honors - Chapter 8 – Right Triangles and Trig – Study Guide
1. Find the geometric mean between:
a. 7 and 12b. 25 and 36
2 – 3: Find the values of x, y, and z.
2.3.
4 – 5: Find the value of x:
4.5.
6. Determine whether the set of number can form a triangle. If so, then determine if the triangle is acute, right or obtuse.
a. 3, 8, 10b. 5, 12, 13c. 7, 8 15d. 65, 72, 88
7. The length of a diagonal of a square is 15 inches. Find the perimeter and area of the square.
8. An equilateral triangle has side length of 10. What is the length of the altitude of the triangle?
9. If the perimeter of a square is 60 inches, find the exact length of each diagonal.
10 – 12: Find the values of x and y.
10.11.12.
13 – 15: Use the triangle with right angle N to find the following trig ratios:
13. (a) sin M14. (a) cos M15. (a) tan M
(b) sin A (b) cos A (b) tan A
16 – 18: Find the exact value of the following trig ratios:
16. (a) sin 45(b) cos 45(c) tan 45
17. (a) sin 30(b) cos 30(c) tan 30
18. (a) sin 60(b) cos 60(c) tan 60
19 – 20: Find the measure of each angle to the nearest whole number
19. tan A = 0.267820. sin B = 0.7986
21. If tan x = 12/5, find the sin x and cos x.
22. If the legs of a right triangle are 3 and 4, find the cos x, sin x, and tan x if x is the smallest angle in the figure.
23. The slide at the playground has a height of 6 feet. The base of the slide is measured on the ground to be 8 feet. What is the length of the sliding board? Then find the angle of elevation the slide makes with the ground.
24. During a football play, a receiver runs a straight route 40 yards up the sideline before turing around to catch a pass from the quarterback. On the opposing team, a defender who started 20 yards across the field from the receiver saw the play setup and ran a slant route towards the receiver. What was the distance the defender had to run to get to the spot where the receiver caught the ball?
25 - 30: Set up the following word problems and solve for the given. Use trig functions and make sure to DRAW IT OUT!
25. Dante is standing at horizontal ground level with the base of the Empire State Building in New York City. The angle formed by the ground and the line segment from his position to the top of the building is 48.4. The height of the Empire State Building is 1472 feet. Find his distance from the Empire State Building to the nearest foot.
26. A rocket ship is two miles above sea level when it begins to climb at a constant angle of 3.5 for the next 40 ground miles. About how far above sea level is the rocket ship after its climb?
27. A dog chasing some birds in the woods got away for its owner. If the owner is 30 feet lower tan the dog and the angle of elevation from the owner to the dog is 10, find the distance from the owner to the dog.
28. A ski slope is 250 yards long with a vertical drop of 100 yards. Find the angle of depression of the slope.
29. To estimate the height of a tree she wants removed, Mrs. Long sights the tree’s top at a 70 degree angle of elevation. She then steps back 10 meters and sights the top at a 26 degree angle. If Mrs. Long’s line of sight is 1.7 meters above the ground, how tall is the tree to the nearest meter?
30. Two buildings are sited from atop a 200-meter skyscraper. Building A is sited at a 35 degree angle of depression, while Building B is sighted at a 36 degree angle of depression. How far apart are the two buildings to the nearest meter?