Question

A vertical pole is standing on a slope that is inclined at an angle 8 degrees to the horizontal and casts a shadow that is 82 ft. long down the slope. How tall is the pole if the angle of elevation of the sun is 28 degrees?

Answer 1

Draw a diagram. If the pole has height h, and the tip of the shadow is x horizontally away from the pole, then

(82 sin8° + h)/x = tan28°
x/82 = cos8°

Now, eliminate x to get

(82 sin8° + h)cot28° = 82 cos8°

Now just solve for h