Question

A tree on a hillside casts a shadow 215 ft down the hill. If the angle of inclination of the hillside is 22???? to the horizontal and the angle of elevation of the sun is 52????, find the height of the tree.

Answer 1

Answer:

H=174.168ft

Explanation:

See diagram below.

First, calculate y using sine function:

$sin(22)=\frac{y'}{215} \\y'=215sin(22)=80.540ft$

Then, calculate x using cosine function:

$cos(22)=\frac{x}{215} \\x=215cos(22)=199.345ft$

Now use tangent to calculate y:

$tan(52)=\frac{y+y'}{x} \\y=x*tan(52)-y'\\y = 174.168ft.$