Date: A

Pre-AP Geometry Review: Trigonometry

Write the trigonometric ratios in lowest terms. Ratio:

1. SmX= So ^ 15 2. Sin Y = 5̂ ~ £g

3. CosX = 5g- 25 4 . C 0 S Y - 5 0 - g

5. TanX = 6. Tan Y = n — ^ Use your calculator to find trigonometric ratios and round to the nearest hundredth 7. sin 58° - , 8. cos 23° ^ ,92- ~ " * 9. tan 51° =_L_23 --"^

I Use your calculator to find the angle measures to the neares^enth^f a degree. | 10.sm-\0.65)cJiO.S ii.cos-^(0.35)= (pQ.S i2.tan-^(18.gt..g> '

^n^^^tli^fmssin^arts^o^^^e/^^ .^^^hl^w^^iw^^^IDip^((l^f^. ^ ^ " l • ^ )TI Round all sides to the nearest tenth and all angles to the nearest degree. ArPi" A- ~ — ' Pictures are not drawn to scale.

13.AC= 4JT\

[^3 = {^^6. Area of the tnangle:^ ^^^^ ^ %iH

. 17. Perimeter of the triangle:

14. Z A = 15. Z B

Find the value of x. Round sides to

1-8. • ' ,'>VP ' :

to tlie near^t humlTCaTn, and angles to the nearest degree. S\n2Q =

^ 6 ?

Not drawn to scale ^4i.'

20.

learest degree.x '"L* ^

Not drlMi''tA s^le

15 OBJ^ Not drawn to scale

. 22. ,

J 17 yd

Not drawi^^scale |

/C X V, • . %

opp opp

1

24. cos ie>=ii

11

Not drawn to scale p.^ni­

ls. Can you find the perimeter of this triangle?

C0S2.I - J L K 13

13CosZl- X -

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26. A ranger spots a forest fire while on a 26 meter observation tower. The angle of depression from the tower to the fire is_12°. To the nearest meter, how far is the fire from the base of the tower?

' i - ^ ^ - — - fan 1 2 = ^

27. 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.

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28. An observer on a cliff 1000 dm above sea level sights two ships due east. The angles of depression of the ships are 47 °and 32°. Find to the nearest decimeter, the distance between the ships. ^ - i / M A

twH7--lMn.' imn-'im " V

29. Two buildings are 100 dm apart across a street. A sunbather at point P finds the angle of elevation of th ; roof of the taller building to be 25° and the angle of depression of its base to be 30°. Find the height of the taller building to the nearest decimeter.

P • • • • • • •

n

100 dm

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i. r i

X 30. A hot air to the balloon

is tied to a pole, which is 7 feet above the ground. The angle of elevation from the pole '9°. I f the amount of rope let out is 105 feet, how high above the ground is the balloon?

IDS l o B . O l - 110.01 lD5S^rn^^\03.01 ^ v ^ A / w v

31. The largest Egyptian pyramid is 146.5 m high. When Rowena stands far away from the pyramid, her line of sight to the top of the pyramid forms an angle of elevation of 20° with the ground. What is the horizontal distance between the center of the pyramid and Rowena? Round to the nearest meter. •1

HUSm 4o3 m

32. 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. Roun^ tp the nearest degree.

"TO ^ Find the geometric mean between each pair of numbers. 33. 28 and 7 ^ 2 ^ ^ yC^ X ' ^ l ^ k 34. 14 and 25

X ^ 7 35. Findx,>', andz 36. Findx, and z.

2-5 ^=v/35b

r

C -

A

10

5 /

37. Findy^^and^z 38. Find x, y, and z

z^=in i l ^ i L

7 . - qt,

:^iilS £ -J4fc ' l i y i

Use the Law of Sines to find each measure. Round lengths to the nearest tenth and angle measures to the nearest degree. 39. ; 40.

7 cm J> _ -7 S i n W , : . S in50 gT^qi sihSO

t3C

of Cos I

s;n''(. 5412.)^33

Use the Law of Cosines to find each measure. Round lengths to the nearest tenth and angle measures to the nearest degree. > 1 > . 1 * 41. . 42.

3.5 in, S id^

^ 1/

fl.?/. ^ / COS"' (.35°il)~lk3

6.2 yd

43. Find the unknown measures in AFGD. (Round to the nearest decimal when necessary.) cos"

Sinl5 S?n5&

S i n 5 8

'̂ ^ 44. Find the unknown measures in ABC. (Round to the nearest decimal or degree when necessary.)

t - 41

Sin4A= 35SiAVB)«,,g,i)75

Sin-'(,W5)^58*'

45. Find the unknown measures in ABC. Rotmd to the nearest degree.

B 47 in.

46. Can you find the area of the triangle above? Yes

M l 3= 721.0^

47. Given A45C with & = 6 meters, c = 10 meters, and ?«ZJ = 42°, find the length of side o_. (Round to two

decimal places.) B|v ' lO^f Ic"̂ ' X (\0')(,1<.")C'O^H2°

48.Find x, to the nearest tenth.

21.5 cm

^ 2 - = 3 ^ 2 + 2 ( 5 q y H l ) C o s 7 q '

2.1.5^+- 50,<^^

X-x/iTzS-S-^-4(0.1 H

J

-1 \

4*

( rHj{ iF)x i b

•\ ^ r '<r JL^P^ruZ X r——

Te

$ p ' M -

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