From a hot air balloon 2 km​ high, a person looks east and sees one town with angle of depression of 16 degrees. He then looks west to see another town with angle of depression of 84 degrees. What is the distance between the two towns ?

1 Answer
P dilip_k
May 15, 2018

Let G be the point on the ground vertically bellow the position of the balloon at B and the positions of towns on the ground are at E and W situated at East and West respectively.

So #angleBEG=16^@andangleBWG=84^@#
And #BG=2km#

Now #(GE)/(BG)=cot16^@#

And #(GW)/(BG)=cot84^@#

So

#EW^2=GE^2+GW^2#

#=>EW^2=BG^2cot^2 16^@+BG^2cot^2 84^@#

#=>EW=BGsqrt(cot^2 16^@+cot^2 84^@)#

#=>EW=2sqrt(cot^2 16^@+cot^2 84^@)~~7#km

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