Geometry Chapter 7 Final Review Answer Key

Geometry CP Chapter 7 Final Review Name: Find the unknown side length. Write your answer in simplest radical form. 1. x = 13 2. x = 72 3. x = 39 4. x = 12 Find the indicated value. Write your answer in simplest radical form. 5. Randy made a ramp for his dog to get into the bed of his truck. The ramp is 6 ft long and the bed of the truck is 3 ft above the ground. Approximately how far from the back of the truck does the ramp touch the ground? A. 3 ft B. 4 ft C. 5.2 ft D. 6.7 ft 6. Find the area of the isosceles triangle with side lengths 20 in., 20 in., and 24 in. Area = 96 in² 7. Find the altitude. Then find the area of the isosceles triangle. [Image of an isosceles triangle with base 28 and height h] h = 24 Area = 336 sq units Find the similarity ratio of the side lengths. 8. 7, 11, and 3/17 9. 2, 2, and 5/2 10. 4.1, 9.2, and 5.6 11. [Image of two similar triangles] Similarity ratio: 20/11 12. [Image of two similar triangles] Similarity ratio: 10/8 = 5/4 13. [Image of two similar triangles] Similarity ratio: 2√10 / 4√10 = 1/2 14. Identify the similar triangles in the diagram. [Image of a diagram with triangles] ΔDEF ~ ΔGHI 15. Identify the similar triangles in the diagram. [Image of a diagram with triangles] ΔABC ~ ΔDBE 16. Find the value of a. [Image of a diagram with triangles] a = 6 17. Skip! 18. Find the values of y, KL, and KM. [Image of a diagram with triangles] y = 15 KL = 15 KM = 15√2 19. Find the values of y, XZ, YZ, and XY. [Image of a diagram with triangles] y = 26 XZ = 26 YZ = 26√2 XY = 52 Using special right triangles, find the values of the variable(s). Write your answer(s) in simplest radical form. 20. Find the value of the hypotenuse. [Image of a right triangle with legs 12 and 12] Hypotenuse = 12√2 21. Find the value of the hypotenuse. [Image of a right triangle with legs 10√2 and 10√2] Hypotenuse = 20 22. ΔMNP is a right triangle. Find the length of MP. [Image of a right triangle with legs 18 and 18] A. 18 in. B. 9√2 in. C. 36 in. D. 18√2 in. 23. [Image of a right triangle with legs 15 and x] x = 15 24. [Image of a right triangle with legs 8 and x] x = 8√3 25. A kite is attached to a 100-foot string as shown in the diagram. How far above the ground is the kite when the string forms the given angle? 1   1. mi01000971.schoolwires.net mi01000971.schoolwires.net [Image of a right triangle with hypotenuse 100 and angle 45 or 30 degrees] A. m∠1 = 45° B. m∠1 = 30° Using special right triangles, find the three trig functions of 45°. 26. [Image of a right triangle with legs 1 and 1] sin(45°) = √2/2 cos(45°) = √2/2 tan(45°) = 1 27. Using a special right triangle, find the three trig functions of 30°. [Image of a right triangle with sides 1, √3, and 2] sin(30°) = 1/2 cos(30°) = √3/2 tan(30°) = √3/3 28. Find all three trig functions of angle B. [Image of a right triangle with sides 3, 4, and 5] sin(B) = 3/5 cos(B) = 4/5 tan(B) = 3/4 29. Find all three trig functions of angle P. [Image of a right triangle with sides 15, 36, and 39] sin(P) = 15/39 = 5/13 cos(P) = 36/39 = 12/13 tan(P) = 15/36 = 5/12 30. Find all three trig functions of angle F. [Image of a right triangle with sides 40, 75, and 85] sin(F) = 40/85 = 8/17 cos(F) = 75/85 = 15/17 tan(F) = 40/75 = 8/15 31. If y = 12 and x = 6, find sin X to the nearest tenth. [Image of a right triangle with sides x, y, and 12] sin(X) = 6/12 = 0.5 Find the value of the variable to the nearest tenth. 32. Find the height (x) of the flagpole to the nearest foot. [Image of a right triangle with height x and base 24] tan(49°) = x/24 x ≈ 27 feet 33. A lamppost is 11 feet tall. If the angle of elevation through the top of the lamppost to the sun is 49°, about how far is the top of the lamppost from the tip of its shadow? [Image of a right triangle with height 11 and angle 49°] tan(49°) = 11/x x ≈ 9.3 feet 34. A rope, staked 20 feet from the base of a building, goes to the roof and forms an angle of 58° with the ground. How long is the rope? [Image of a right triangle with base 20 and angle 58°] sin(58°) = 20/x x ≈ 23.6 feet 35. A road rises 10 feet in a horizontal distance of 200 feet. What is the angle of elevation? tan(θ) = 10/200 θ ≈ 2.86° 36. If a = 17 and m∠A = 31°, find b. [Image of a right triangle with side a = 17 and angle A = 31°] sin(31°) = b/17 b ≈ 8.7 37. Find x. [Image of a right triangle with hypotenuse 50 and angle 45°] x = 50/√2 = 25√2