Question

The press box at a baseball park is 32.0 ft above the ground. A

reporter in the press box looks at an angle of 15.0° below the
horizontal to see second base. What is the horizontal distance
from the press box to second base?

Answer 1

To find the horizontal distance from the press box to second base, we can use trigonometry. The tangent of an angle is equal to the opposite side divided by the adjacent side. Therefore, the horizontal distance from the press box to second base is approximately 120.4 ft.

Step-by-step explanation:

To find the horizontal distance from the press box to second base, we can use trigonometry. Since the reporter is looking at an angle of 15.0° below the horizontal, we can consider the angle of elevation to be 15.0°.

We can then use the tangent function to find the horizontal distance. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the adjacent side is the horizontal distance we are trying to find, and the opposite side is the height of the press box.

Let's calculate the horizontal distance:

tan(15.0°) = opposite/adjacent

tan(15.0°) = 32.0 ft/x

x = 32.0 ft / tan(15.0°)

x ≈ 120.4 ft

Therefore, the horizontal distance from the press box to second base is approximately 120.4 ft.

Answer 2

First we can find angles of triangle which vertices are: press box at 32ft, point on the ground directly bellow press box and second base.

The angle at second base is:
180-90-(90-15) where 90 - 15 is the angle at press box vertex.

angle at second base is: 15.

tan(15) = 32/x where x is our unknown distance.
x = 32/tan(15) = 119.42 feet