Question 16962
You can readily solve this problem using elementary trigonometry.

Knowing that the angle of elevation from the observer on the ground to the top of the tower is 62 degrees, and knowing that the observer is 150 feet from the base of the tower, you can use the tangent function to find the height, h, of the tower. In the right triangle formed by the tower (vertical leg = h) and the distance of the observer from the base of the tower (base of the right triangle = 150 ft.), the tangent of the angle of elevation , A, is given by:

{{{tan(A) = h/150}}} Multiply both sides by 150.
{{{h = (150)tan(A)}}} Angle A = 62 degs.
{{{h = (150)tan(62)}}} Tan(62) = 1.88
{{{h = (150)(1.88)}}}
{{{h = 282}}}

The tower is 282 feet tall.