Question

At a certain time of day the angle of elevation of the sun is 80 degrees. To the nearest foot find the height of a tree whose shadow is 40 feet long.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

angle of elevation = 80°

shadow of the tree = 40 ft

Step 02:

right triangle:

tan α = opposite / adjacent

α = 80°

opposite = height of the tree = x

adjacent = shadow of the tree = 40 ft

tan 80° = x / 40 ft

40 ft * tan 80° = x

226.85 ft = x

The answer is:

height of the tree = 227 ft