Problem 75 - Algebra and Trigonometry

Question

A tower that is 125 feet tall casts a shadow 172 feet long. Find the angle of elevation of the Sun to the nearest degree.

Step-by-Step Solution

Answer

The angle of elevation of the Sun is approximately 36 degrees.

Step 1: Identify Given Information

Based on the problem, the tower represents the opposite side with a length of 125 ft and the shadow represents the adjacent side with a length of 172 ft.

Step 2: Apply the Tangent Formula

The formula for tangent is \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\). Plug in the values: \(\tan(\theta) = \frac{125}{172}\).

Step 3: Solve for angle

Now, solve for \(\theta\) using the inverse tangent function. Therefore, \(\theta = \tan^{-1}(\frac{125}{172})\). The angle should be calculated in degrees.

Step 4: Round to the Nearest Degree

Since the problem asks for the angle of elevation to the nearest degree, make sure to round the final answer.