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Trigonometry Week 13 Test Grade Report

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Trigonometry

Type

Exam Practice

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tnyyneqb_101

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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

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

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%)° .

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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

47.58°47.58°

≈

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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Tags: trigonometry triangle formula angle of depression law of cosines vertical component