Geometry
Review – Unit 7 Trigonometry
Name ________________________
The lengths of three sides of a triangle are given. Describe each triangle as acute, right, or obtuse.
1) 18, 80, 82
2) 6, 12, 16
3) Is 5, 20, 21 a Pythagorean Triple?
Using the special right triangle rules, find x and y. If necessary, give answers in simplest radical form.
4) x = ________
y = _________
6) x = ________ y = _______
5) x = _________ y = __________
7) x = _______ y = _________
8) x = _________ y = _____________
9) Express sin T, cos T, and tan T as ratios.
sin T = ___________
cos T = ___________
tan T = ___________
10)
sin(38o) = cos(?)
_________o
11) Choose a, b, or c to complete the statement. Then use the lines below to explain why your choice is correct.
cos(K) =
a) tan(M)
b) cos(M)
c) sin(M)
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For Questions # 12-17, find the value of x. Round lengths of segments to the nearest tenth and angle measures to the
nearest degree.
12)
13)
14)
x = _________
x = _________
x = _________
15)
16)
17)
x = _________
x = _________
x = _________
18) Twenty minutes after being launched, a hot-air balloon is at an altitude of 300m. The pilot can still see the starting
point on the ground at a 25o angle of depression. How long is the line of sight from the starting point to the balloon?
Round your answer to the nearest hundredth. (Draw a picture and label.)
19) A captain of a sailboat sights the top of a light house at a 17o angle of elevation. A navigation chart shows the height
of the lighthouse to be 120 m. How far is the sailboat from the lighthouse? Round your answer to the nearest hundredth.
(Draw a picture and label.)
20) Students in a hang gliding class stand on the top of a cliff 70 m high. They watch a hang glider land on the beach
below. The angle of depression to the landed hang glider is 72o. How far is the hang glider from the base of the cliff.
Round your answer to the nearest hundredth. (Draw a picture and label.)
21) Find the area of the triangle:
Round your answer to the nearest hundredth.
22) Multiple Choice. Which expression can be used to
find the length of b?
a)
c)
15
sin 38 o
15
tan 38 o
23) Use the Law of Sines to find the length c. Round your answer to the nearest hundredth.
24) Use the Law of Cosines to find m  C. Round your answer to the nearest hundredth.
b) 15sin 38o
d) 15 tan 38o