Pre AP Geometry Chapter 9 Review Name

9.1 The Pythagorean Theorem and Radicals All answers must be in simplified radical form ^

1. V28 - 5V63 + 2V252 . : 4,_J_,v/iS- 3 JiS -/ vil3

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5. J[5

î md the valueof x. Then tell whether the side lengths form a Pythagorean triple. (Answers in Simplest radical form) v

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9.2 Special Right Triangles 1 Express your answers in simplest radical form.

OT tne mi.

45X̂ y c

ismR variaoies.

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16. Each triangle is a 452-452-90^ triangle. Find the value of x. MS X

45 gle. Fin

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2.

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BD =

Find m ZADB=

AC = 35

C Bp BC •X:ml2.X 3Ji

30 D AD

boiqo 2J^ 3j2 3vJt.

2^ 30 1 1J3 IM

30 qo X 2X 7 7J3 14-

19. An eaullateral triangle has an altitude of 21 inches. What is the side length of the triangle?

20. The length of a diagonal of a square is 24 ^/2 millimeters. Find the perimeter and area of the square. H5 X

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i 9.3 Geometric Mean Express your answers in simplest radical form \ Find^e ^ometric mean of: , ^ ,̂

21 b

22. 36 and 8

Find X, y, and z r« _ ^

23. 14 and 25

=̂1- x̂ îee a.A

i = \/iTT

9.4-9.5 Trigonometric Functions

Write the trigonometric ratk ŝ in lowest terms. Fraction(Ratio)

; , 26.SinX= 5g 27. Cos X = 5^ H 25 /28. Tan X = l|g "

14

Use your calculator to find trigonometric ratios and round to the nearest hundredth Cp]oOj\4")n .J 29. sin 58° „ 9)5 30. cos 23° » ^ 2. 31. tan 51° _U23_ ^ Use your calculator to find the angle measures to the nearest degree. C]y^^rC\~£,-t. -fijincVJ OlO " ZIl, } 32.sm-^(0.65)_Ly_* 33005-^(0.35) -/Q^ 34tan-^(18.1)

44. Jessie is building a ramp for loading motorcycles onto a trailer. The trailer is 2.8 feet off of the ground. To avoid making it too difficult to push a motorcycle up the ramp, Jessie decides to make the angle between the ramp and the ground 15°. To the nearest hundredth of a foot, find the length of the ramp.

Sin 15 45. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is 10 yards tall casts a shadow 14 yards long. Round to the nearest degree.

Angles - inverse pid^

46. You and another person are sunbathing on the beach near a lifeguard station. The other person chooses a spot that is the same distance from the shoreline but 30 feet closer to the station than you. The angles of elevation from you and the other person to the top of the lifeguard station are 26° and 51°, respectively. Estimate the heijght of,the (î fegû rd station to the nearest tenth of a foot

5S.Z

eguard station are 26° and 51°, respectively. Estimate the height of the lifeguard ^

31.1 SinZlo- JL,

S5.Z 2SinZlo=^ X - 2M.Z]

47. An observer on a cliff 1000 m above sea level sights two ships due east. The angles of depression of the ships are 47 "and 32°. Find to the nearest tenth of a meter, the distance between the ships. —j-^ -ft KVcl S^^^

- To ftrs\- sVup'o X To iecona SKAV' J Su\)iroLC^ ̂ ^^0^^ Tan 41= iOQP Jay^ 5r=

48. A hot air balloon is tied to a pole, which is 7 feet above the ground. The angle of elevation from the pole to the balloon is 79°. If tJae amount of rope let out is 105 feet, to the nearest foot, how high above the ground is the balloon?

5pp n o t 1 . \oS

\ o 5 a n i q ' = x =t 103,07 + 1-C-l--1110-f-V 49. In an obstacle course, participants climb to the top of a tower and use a zip line to travel across a mud pit. The zip line extends from the top of a tower to a point on the ground 29.2 feet away from the base of the tower. The angle of elevation of the zip line is 23°. Estimate the length of the zip line to the nearest tenth of a foot. )

Not dratvn to scale i Cos 23 3K1 .̂

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