Question

The press box at a baseball park is 37.5 ft above the ground. A reporter in the press box looks at an angle of 15.5 ∘ below the horizontal to see second base.

What is the horizontal distance from the press box to second base?
Express your answer using three significant figures.

Answer 1

Using trigonometry, the horizontal distance from the press box to second base is calculated to be approximately 139 ft by applying the tangent function to the known angle of depression and the vertical height of the press box.

Step-by-step explanation:

To find the horizontal distance from the press box to second base, we can use trigonometry, specifically the tangent function, which relates the angles of a right triangle to its side lengths.

The situation described gives us an angle of depression of 15.5 degrees and a vertical distance (opposite side of the triangle) of 37.5 feet. The horizontal distance (adjacent side of the triangle) can be calculated using the tangent of the angle.

Let d represent the horizontal distance to second base. Using the trigonometric identity:

tangent(angle) = opposite/adjacent

We have:

tangent(15.5 degrees) = 37.5 ft / d

By rearranging the equation to solve for d, we obtain:

d = 37.5 ft / tangent(15.5 degrees)

Using a calculator, we find:

d ≈ 139.336 ft

Therefore, the horizontal distance from the press box to second base is approximately 139 ft, when expressed using three significant figures.