Question

From a point on the bank of a stream,the angle of elevation of a tree top on the opposite bank is 38 degrees and 23 mins. And from a point 200.6 ft. straight back from the bank, the angle of elevation of the tree top is 20 degrees and 22 mins. Find the height of the tree and the width of the stream? thanks in advance.

Answer 1

Draw a diagram, looking along the stream. If the width of the stream is w, and the height of the tree is h, then

h/w = tan38°23'
h/(w+200.6) = tan20°22'

Eliminating w, we have

h*cot38°23' = h*cot20°22' - 200.6
h = 200.6/(cot20°22' - cot38°23')
Now, having h, you can evaluate w.