Problem 48 - Precalculus Essentials

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 81.0 degrees.

Step 1: Identify the Opposite and Adjacent sides in the triangle

In a right triangle, the Opposite side to the angle being considered is the height of the building (250ft) and the Adjacent side is the shadow (40ft).

Step 2: Use the formula for tangent

The tangent of an angle in a right triangle is given by the ratio of the Opposite side to the Adjacent side. So here, \(\tan(θ) = \frac{250}{40}\)

Step 3: Calculate the angle

To get the angle of elevation, we need to find the inverse tangent (or arctan) of the value we found in Step 2. In calculation, we get \(θ = \arctan(\frac{250}{40})\)

Step 4: Convert the angle to degrees

Finally, to find the angle in degrees as the exercise requires, using the calculator convert the radians to degrees. And round the answer to the nearest tenth.