Questions: A tower that is 132 feet tall casts a shadow 174 feet long. Find the angle of elevation of the sun to the nearest degree. The angle of elevation is degrees. (Round to the nearest degree.)

A tower that is 132 feet tall casts a shadow 174 feet long. Find the angle of elevation of the sun to the nearest degree.

The angle of elevation is degrees. (Round to the nearest degree.)

Transcript text: A tower that is 132 feet tall casts a shadow 174 feet long. Find the angle of elevation of the sun to the nearest degree. The angle of elevation is $\square$ degrees. (Round to the nearest degree.)

Solution

Solution Steps

Step 1: Identify the given information

The height of the tower (opposite side) is 132 feet, and the length of the shadow (adjacent side) is 174 feet. We are looking for the angle of elevation of the sun, which is the angle between the ground and the sun's rays.

Step 2: Set up the trigonometric equation

We can use the tangent function to relate the angle of elevation, the opposite side, and the adjacent side in a right triangle: \$\tan(A) = \frac{\text{opposite}}{\text{adjacent}}\$ where A is the angle of elevation.

Step 3: Plug in the given values

\$\tan(A) = \frac{132}{174}\$

Step 4: Solve for the angle

To find the angle A, we take the inverse tangent (arctan) of both sides: \$A = \arctan(\frac{132}{174})\$ \$A \approx \arctan(0.7586)\$ \$A \approx 37.15^{\circ}\$

Step 5: Round to the nearest degree

Rounding to the nearest degree, we get: \$A \approx 37^{\circ}\$