Question

At a certain time, the shadow of a lamppost is 6 ft and the actual height of the lamppost is 15 ft. What is the angle of depression of the sun? Round the angle to the nearest degree.

Answer 1

Task. At a certain time, the shadow of a lamppost is 6 ft and the actual height of the lamppost is 15 ft. What is the angle of depression of the sun? Round the angle to the nearest degree.

Solution. Consider the following figure

The angle $x$ is called the angle of depression. It follows from the right triangle $ABC$ that

$\tan x=\frac{BC}{AB}=\frac{15}{6}=2.5$

Hence

$x=\arctan(2.5)\approx 68.2{}^{\circ}\approx 68{}^{\circ}.$