Answer:
14. 61.2 mi N, 49.8 mi W
15. 7.3 ft
Explanation:
14. The components in the different directions are found using the sine and cosine functions. (Draw yourself a diagram to help see this.)
north distance = (78.9 mi)cos(39°10') ≈ 61.2 mi
west distance = (78.9 mi)sin(39°10') ≈ 49.8 mi
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15. Let d represent the distance from the observation point to the door. Then ...
8.8 ft = d·tan(56°)
x = d·tan(51°)
Dividing the second of these equations by the first cancels d and gives ...
x/(8.8 ft) = tan(51°)/tan(56°)
Multiplying by 8.8 ft, we can find x:
x = (8.8 ft)(tan(51°)/tan(56°)) ≈ 7.3 ft