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
SCooke
May 12, 2018

#7.18km#

Explanation:

The angle of depression is the angle below horizontal that an observer must look to see an object that is lower than the observer. Note: The angle of depression is congruent to the angle of elevation (this assumes the object is close enough to the observer so that the horizontals for the observer and the object are effectively parallel.
http://www.mathwords.com/a/angle_depression.htm

So, at a height of 2km, we have two triangles. One with base length of #tan(16) = 2/x_1# and the other with a base length of #tan(84) = 2/x_2#.
#x_1 = 6.97#
#x_2 = 0.21#
Thus, the total distance between the two towns is #x_1 + x_2 = 6.97 + 0.21 = 7.18km#

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