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) About Me  (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 39%5Eo and when he moved to A, 100 m away from the mountain, the angle of elevation became 38.2%5Eo.

So, in the figure, AD = 100 m; < BAC = 38.2%5Eo; < BDC = 39%5Eo

In right-angled triangle ABC,
BC%2FAB+=+tan%2838.2%5Eo%29
or AB+=+BC%2F%28tan%2838.2%5Eo%29%29 _____(1)

In right-angled triangle DBC,
BC%2FDB+=+tan%2839%5Eo%29
or DB+=+BC%2F%28tan%2839%5Eo%29%29 _____(2)

Subtracting (2) from (1) we have
AB+-+DB+=+BC%2Ftan%2838.2%5Eo%29+-+BC%2Ftan%2839%5Eo%29
or AD+=+BC%28cot%2838.2%5Eo%29+-+cot%2839%5Eo%29%29
or BC+=+AD%2F%28cot%2838.2%5Eo%29+-+cot%2839%5Eo%29%29
or BC+=+100%2F%281.270773+-+1.234897%29
or BC = 2787.4 m (approx) = 2.7874 km

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