Download Mod 2 Test 3 - Lessons 26

Name: __________________________
Date: ____
Regents Geometry
Module 2, Test 3: Lessons 26 – 34
Score: _____ / _____
1. Answer the following questions based on the diagram below.
Find the sine, cosine, and tangent values of angles r and s. Leave answers as fractions.
a. sin r =
b. sin s =
c. cos r =
d. cos s =
e. tan r =
f. tan s =
2. Determine the measure of b to the nearest tenth of a degree.
3. A ball is dropped from the top of a 45 ft. building. Once the ball is released a big gust of wind comes
along and blows the ball off course. It lands 4 ft. from the base of the building.
a. Draw a diagram to the right of this situation,
specifically labeling the side lengths given in
the word problem.
b. By approximately how many degrees was the
ball blown off course? Round your answer to
the nearest degree.
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4. Find the values of  that make each statement true.
a. sin  = cos 32
b. cos  = sin ( + 20)
5. A radio tower is anchored by long cables called guy wires, such as AB in the figure below. Point A is 250
m from the base of the tower, and BAC = 59˚.
a. How long is the guy wire? Round to the nearest tenth.
b. How far above the ground is it fastened to the tower?
c. How tall is the tower, DC, if DAC = 71˚?
̅̅̅̅̅ connects side ̅̅̅̅
6. In right triangle ABC with B a right angle, a line segment 𝐵’𝐶’
𝐴𝐵 with the hypotenuse
so that AB’C’ is a right angle as shown. Use facts about similar triangles to prove cos C’ = cos C.
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7. LMN is a 30-60-90 right triangle. Find the unknown lengths x and y.
8. The line on the coordinate plane makes an angle of depression of 24˚. Find the slope of the line, correct
to four decimal places.
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9. If sin  = 3 , use trigonometric identities to find cos  and tan .
10. Given two sides of the triangle shown, having lengths of 3 and 7, and their included angle of 49˚, find
the area of the triangle to the nearest tenth.
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11. Use the law of sines to find lengths b and c in the triangle below. Round answers to the nearest tenth
as necessary.
12. Given DEF, use the law of cosines to find the length of the side marked d to the nearest tenth.
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