# Trigonometry Week 13 Test Grade Report

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Subject
Trigonometry
Type
Exam Practice
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Trigonometry Week 13 Test - Grade Report
Score:
80% (80 of 100 pts)
Submitted:
Aug 1 at 7:35am
Question: 1
Grade: 1.0 / 4.0
Find the area of the triangle if a=9a=9inches, b=7b=7inches, and α=32°α=32°. Round to
the nearest tenth.
Area 26.2 (100%) in
2
Solution
Since the triangle is non-right, use the area of an oblique triangle formula.
Area = 12absinγ12absinγ
Use the Law of Sines to find ββ and then use the Triangle Sum Theorem to find γγ.
sin32°9=sinβ7sin32°9=sinβ7
sinβ=7sin32°9sinβ=7sin32°9
β≈24.3°β≈24.3°
γ≈180°−32°−24.3°≈123.7°γ≈180°−32°−24.3°≈123.7°
A≈12(9)(7)sin123.7°≈26.2066...≈26.2A≈1297sin123.7°≈26.2066...≈26.2in
2
Question: 2
Grade: 1.0 / 4.0

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Solution
Use the law of cosines to find the angle.
c2c2
=
a2+b2−2abcosCa2+b2−2abcosC
302302
=
382+152−2(38)(15)cosx382+152−2381
5cosx
900900
=
1,444+225−1,140cosx1,444+225−1,140c
osx
900−1,444−225−1,140900−1,444−225−
1,140
=
cosxcosx
−769−1,140−769−1,140
=
cosxcosx
cos−17691,140cos−17691,140
=
xx
47.58°47.58°
xx
Question: 3
Grade: 1.0 / 4.0
What are the components of a vector with magnitude 62–√62 and a direction angle
of 45°45°?
Enter the horizontal component in the first box and the vertical component in the second box.
6 (50%) , 6 (50%)
Solution
Graph the vector.
Find y,y, the vertical component.

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Trigonometry Week 13 Test - Grade Report Score: 80% (80 of 100 pts) Submitted: Aug 1 at 7:35am Question: 1 Grade: 1.0 / 4.0 Find the area of the triangle if a=9a=9inches, b=7b=7inches, and α=32°α=32°. Round to the nearest tenth. Area ≈≈26.2 (100%) in2 Solution Since the triangle is non-right, use the area of an oblique triangle formula. Area = 12absinγ12absinγ Use the Law of Sines to find ββ and then use the Triangle Sum Theorem to find γγ. sin32°9=sinβ7sin32°9=sinβ7 sinβ=7sin32°9sinβ=7sin32°9 β≈24.3°β≈24.3° γ≈180°−32°−24.3°≈123.7°γ≈180°−32°−24.3°≈123.7° A≈12(9)(7)sin123.7°≈26.2066...≈26.2A≈1297sin123.7°≈26.2066...≈26.2in2 Question: 2 Grade: 1.0 / 4.0 A Geiger counter is vvfeet above a sample of radium in a stairwell and ss feet along the stairs away from directly above the substance. If based on the counter readings the radium is dd feet away, find xx, as shown in the picture, given v=30,s=15,v=30,s=15,and d=38d=38. Round to the nearest hundredth. The angle of depression from the stairs to the substance is approximately 47.58 (100%)° . Solution Use the law of cosines to find the angle. c2c2 = a2+b2−2abcosCa2+b2−2abcosC 302302 = 382+152−2(38)(15)cosx382+152−2381 5cosx 900900 = 1,444+225−1,140cosx1,444+225−1,140c osx 900−1,444−225−1,140900−1,444−225− = 1,140 cosxcosx −769−1,140−769−1,140 = cosxcosx cos−17691,140cos−17691,140 = 47.58°47.58° Quest ...
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