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Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H=60°, and from a second position L=20 feet farther along this path it is B=50° What is the height of the​ tree?

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Answer: 44.11 feets

Step-by-step explanation:

Using Pythagoras :

tan θ = opposite / Adjacent

Tan 60° = h / x

h = x tan 60 - - - (1)

tan 50° = h / (x + 20)

h = (x + 20) tan 50 - - - (2)

Equate (1) and (2)

x tan60 = (x + 20) tan 50

1.73205x = (x + 20) 1.19175

1.73205x = 1.19175x + 23.835

1.73205x - 1.19175x = 23.835

0.5403x = 23.835

x = 23.835 / 0.5403

x = 44.114380

Hence, height = 44.11 feets

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