# Trigonometry

posted by Gab

4. An observer is near a river and wants to calculate the distance across the river. He measures the angle between his observations of two points on the shore, one on his side and one on the other side, to be 28º. The distance between him and the point on his side of the river can be measured and is 300 feet. The angle formed by him, the point on his side of the river, and the point directly on the opposite side of the river is 128º. What is the distance across the river?

1. Steve

Assuming that the first-named point on the opposite side (P) is the point directly opposite from the point on his own side (Q), then we have, if the observer is point O,

m<POQ = 28
m<OQP = 128, so
m<OPQ = 24
Now, using the law of sines, if the width is w, we have

w/sin28 = 300/sin24

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