SOLUTION: An observer measures the angle of evevation to the top of a mountain and obtains a value of 39 degrees. After moving 100m farther away from the mountain,the angle of el

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Question 42272: An observer measures the angle of evevation to the top of a mountain and obtains a value of 39 degrees. After moving 100m farther away from the mountain,the angle of elevation is massured as 38.2 degrees. How tall is the mountain?
Answer by psbhowmick(878)   (Show Source): You can put this solution on YOUR website!


Let the points C and B denote the top and the base of the mountain respectively.
When the person was at D, the angle of elevation was and when he moved to A, 100 m away from the mountain, the angle of elevation became .

So, in the figure, AD = 100 m; < BAC = ; < BDC =

In right-angled triangle ABC,

or _____(1)

In right-angled triangle DBC,

or _____(2)

Subtracting (2) from (1) we have

or
or
or
or BC = 2787.4 m (approx) = 2.7874 km

Hence, the reqd. height of the mountain is 2.7874 km.

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