SOLUTION: a bush walker estimates the angle of elevation to the top of the hill to be 22 degrees. after walking 700metres closer to the hill, the angle of elevation to the top of the hill be

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Question 1173657: a bush walker estimates the angle of elevation to the top of the hill to be 22 degrees. after walking 700metres closer to the hill, the angle of elevation to the top of the hill becomes 38 degrees. Determine the height of the hill?
Answer by ewatrrr(24785) About Me  (Show Source):
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a bush walker estimates the angle of elevation to the top of the hill to be 22 degrees. after walking 700metres closer to the hill, the angle of elevation to the top of the hill becomes 38 degrees.
 

Hi,

Determine the height of the hill:

Letting x be the shorter distance to the Hill and h the height

Using opp/adj  tan(22)  &  tan(38) 

tan(22) = h/(x+700)             and  tan(38) = h/x  0r h =  tan(38)x

Substituting for h

tan(22) =  tan(38)x/(x+700)

tan(22)(x+700)=tan(38)x   

   +700tan%2822%29%2F%28tan%2838%29-tan%2822%29%29+=+x+

Using calculator

 x = 749.5m   and h = 585.7m   h+=++tan%2838%29x

Wish You the Best in your Studies.