Chapter 8 Test Review

I. All answers should be in the form of a whole number or a radical I. All answers should be in the form of a whole number or a radical. (No decimals allowed)   Simplify 24 2. 27 3. 300 100 3 4 6 9 3 2 6 3 3 10 3

4. 54 5. 4 12 + 2 27 −3 3 7. 7 6 = 8. 2 6 2 = 9 6 4 4 3 + 2 9 3 - 3 3 4(2) 3 + 2(3) 3 - 3 3 3 6 8 3 + 6 3 - 3 3 11 3 7 6 • 6 6 = 42 6 6. 5 • 3 15 (2 6 )(2 6 ) = 4(6) = 24

9. Solve for x. a2 + b2 = c2 x2 + 152 = 172 x2 + 225 = 289 x2 = 64 x = 8

a2 + b2 = c2 x2 + 62 = 102 x2 + 36 = 100 x2 = 64 x = 8 units 10. In an isosceles triangle, the base is 12 units long and the legs are 10 units long. Find the length of the altitude to the base. a2 + b2 = c2 x2 + 62 = 102 10 10 x2 + 36 = 100 x x2 = 64 6 x = 8 units 12

hyp = leg 2 hyp = leg 2 8 = x 2 y = 5 2 8 2 = x x = 5, y = 5 2 = 8 2 2 Solve for x and y. 11 12. hyp = leg 2 hyp = leg 2 8 = x 2 y = 5 2 8 2 = x x = 5, y = 5 2 • 2 2 = 8 2 2 x = 8 2 = 4 2 x = 4 2 , y = 4 2

hyp = sl(2) hyp = leg 2 x = 7(2) y = 3 6 2 x = 14 y = 3 12 ll = sl 3 13. 14. y x hyp = sl(2) hyp = leg 2 x = 7(2) y = 3 6 2 x = 14 y = 3 12 ll = sl 3 y = 3 4 3 y = 7 3 y = 3(2) 3 x = 14, y = 7 3 x = 3 6 , y = 6 3

ll = sl 3 15 = x 3 hyp = sl(2) 18 = x(2) 9 = x ll = sl 3 hyp = sl(2) 15. 16. x y ll = sl 3 15 = x 3 hyp = sl(2) x = 15 3 • 3 3 = 15 3 3 18 = x(2) 9 = x x=5 3 ll = sl 3 hyp = sl(2) y = 9 3 y = 5 3 (2) y = 10 3 x = 9, y = 9 3 x = 5 3 , y = 10 3

c2 ___ a2 + b2 262 ___ 102 + 242 right 676 ___ 100 + 576 676 ___ 676 = 17. What type of triangle has sides with the lengths 10, 24, and 26?    18. What type of triangle has sides with the lengths 2 3 , 3, and 6? c2 ___ a2 + b2 262 ___ 102 + 242 right 676 ___ 100 + 576 676 ___ 676 = c2 ___ a2 + b2 62 ___ (2 3 )2 + 32 obtuse 36 ___ 12 + 9 36 ___ 21 >

II. Decimal answers are allowed for some questions in this section II. Decimal answers are allowed for some questions in this section. Be sure to round appropriately. Give the appropriate ratio for #19-21. tan A = ____ sin A = ____ 21. cos A = ____ 12 9 = 4 3 12 15 = 4 5 9 15 = 3 5

Solve for x. (Round to the nearest tenth.) 22. 23. 22. 23. y y tan 35° = 𝑥 12 sin 67°= 𝑥 50 x = (12)(tan 35°) x = (50)(sin 67°) 𝑥≈8.4 𝑥≈46.0 cos 35°= 12 𝑦 cos 67°= 𝑦 50 (y)(cos 35°)=12 y = (50)(cos 67°) 𝑦≈14.6 𝑦≈19.5

tan y°= 8 5 y = 𝑡𝑎𝑛 −1 8 5 y ≈58° 24. 25. Solve for y. cos 63° = 23 𝑥 (x)(cos 63°) =23 𝑥= 23 cos 63° tan y°= 8 5 𝑥≈50.7 tan 63°= 𝑦 23 y = 𝑡𝑎𝑛 −1 8 5 y = (23)(tan 63°) y ≈58° 𝑦≈45.1

20 cos y° = 15 17 tan 32°= 𝑥 20 x = (20)(tan 32°) y = 𝑐𝑜𝑠 −1 15 17 26. Solve for y. 27. Solve for x. 20 cos y° = 15 17 tan 32°= 𝑥 20 x = (20)(tan 32°) y = 𝑐𝑜𝑠 −1 15 17 𝑥 ≈12.5 y ≈ 28°

28. An observer in an airplane at a height of 500 meters sees a car at an angle of depression of 31°. If the plane is over a barn, how far is the car from the barn? (Express lengths correct to the nearest integer.)   tan 31°= 500 𝑥 31° (x)(tan 31°)=500 𝑥= 500 tan 31° 500m 𝑥≈832 m 31° x

29. From a point 340 meters from the base of the Hoover Dam, the angle of elevation to the top of the dam is 33°. Find the height of the dam to the nearest meter? (Express lengths correct to the nearest integer.)   33° tan 33°= 𝑥 340 x = (340)(tan33°) x 𝑥≈221 𝑚 33° 340 m

a2 + b2 = c2 22 + 62 = c2 c 4 + 36 = c2 40 = c2 40 = c 4 10 = c 𝑐=2 10 30. The diagonals of a rhombus have lengths 4 and 12. Find the length of a side in simplest form. (radical answer) a2 + b2 = c2 22 + 62 = c2 c 4 + 36 = c2 6 2 40 = c2 40 = c 4 10 = c 6 2 𝑐=2 10