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From the top of the mountain 532 m higher than a nearby river, the angle of depression of a point P on the closer bank of the river is 52.6o, and the angle of depression of a point Q directly opposite P on the other side is 34.5o. Points P and Q and the foot of the mountain are on the same horizontal line. Find the distance across the river from P to Q.

 May 14, 2020
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The distance, M, from  the base of the mountain to the  nearest bank can be found as

 

tan 52.6  =   532/ M

Rearrange as

M =  532 / tan 52.6  ≈ 406.7 ft

 

The distance,N,  from  the base of the mountain to the far bank can be found as

 

tan 34.5  =  532/ N

N = 532 / tan 34.5  ≈ 774.1  ft

 

The width of the river  =   N - M  =    774.1 - 406.7   ≈  367.4  ft

 

 

cool cool cool

 May 14, 2020

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