The angle of elevation of the sun is . Find the length, l, of a shadow cast by a tree that is 47 feet tall. Round answer to two decimal places.
A) feet
B) feet
C) feet
D) feet
E) feet

Question

The angle of elevation of the sun is  . Find the length, l, of a shadow cast by a tree that is 47 feet tall. Round answer to two decimal places.
A) feet 
B) feet 
C) feet 
D) feet 
E) feet

Quizplus · Accepted Answer

Let's draw a right triangle with the tree, its shadow, and the angle of elevation of the sun.

The height of the tree is the opposite side of the angle, and the length of the shadow is the adjacent side. We want to find the length of the shadow.

We can use the tangent function to solve for the length of the shadow:

tan(11ec1854_fd86_ec57_acfc_ef42aaa394a1_TBX8702_11) = opposite/adjacent
tan(11ec1854_fd86_ec57_acfc_ef42aaa394a1_TBX8702_11) = 47/l

We can rearrange this equation to solve for l:

l = 47/tan(11ec1854_fd86_ec57_acfc_ef42aaa394a1_TBX8702_11)

Using a calculator, we get:

l ≈ 268.15 feet

Rounding to two decimal places, we get choice B: 11ec1854_fd86_ec59_acfc_55fe22c4eaea_TBX8702_11 feet.

The Angle of Elevation of the Sun Is