Answer:
6. (-3/7)√5
7. 22 ft
8. 58°
Explanation:
6. The relationship between sine and cosine is ...
sin(θ)² + cos(θ)² = 1
Solving for sine gives ...
sin(θ) = ±√(1 -cos(θ)²)
In the third quadrant, sine and cosine have the same sign, so ...
sin(θ) = -√(1 -(-2/7)²) = -√(45/49)
sin(θ) = (-3/7)√5
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7. You know from SOH CAH TOA that ...
Sin = Opposite/Hypotenuse
In the relevant triangle, ...
sin(52°) = (kite height)/(28 ft)
kite height = (28 ft)·sin(52°) ≈ (28 ft)(0.78801)
kite height ≈ 22 ft
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8. You know from SOH CAH TOA that ...
Tan = Opposite/Adjacent
tan(θ) = (120 ft)/(74 ft) = 60/37
θ = arctan(60/37) ≈ 58°
The angle of elevation is about 58°.
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Comment on these questions
There are a few trig relationships that it is convenient to remember (or keep handy). SOH CAH TOA covers several of them. The relation shown above between sine and cosine is another, as is the corresponding relation between tangent and secant: tan² +1 = sec².