Problem 48 - Algebra and Trigonometry

Question

A building that is 250 feet high casts a shadow 40 feet long. Find the angle of elevation, to the nearest tenth of a degree, of the Sun at this time.

Step-by-Step Solution

Answer

The angle of elevation of the sun is approximately 80.5 degrees.

Step 1: Identify given values

Given the height of the building (opposite side of the triangle) as 250 feet and the length of the shadow (adjacent side of the triangle) as 40 feet.

Step 2: Applying the Tangent Function

In a right triangle, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. So, \(tan(θ) = \frac{{opposite}}{{adjacent}} = \frac{{250}}{{40}} \) .

Step 3: Computation of the angle

To find the angle of elevation indicated by θ, apply the inverse tangent function or arctan to both sides of the previous equation. Using a calculator, compute \(θ = arctan(\frac{{250}}{{40}}) \).

Step 4: Round the result

Round the result to the nearest tenth to get the final answer.