The press box at a baseball park is 46.5 ft above the ground. A reporter in the press box looks at an angle of 13.1° below the horizontal to see second base. What is the horizontal distance from the press box to second base?

The problem involves trigonometry, specifically the tangent function. The height of the press box above the ground serves as the 'opposite' side in a right triangle, while the horizontal distance from it to second base is the 'adjacent' side we need to find. We solve for this using the angle of depression.

Explanation:

This problem is a practical application of trigonometry, particularly the tangent function. In a right triangle, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side.

Here, the height of the press box from the ground (46.5 ft) represents the opposite side in our right triangle, while the horizontal distance to the second base is the adjacent side we're trying to find. The angle of depression from the reporter to the base (13.1 degrees) is the angle we'll use.

To find the horizontal distance, we rearrange our tangent function to solve for the adjacent side:

Adjacent = Opposite / tan (Angle)

Adjacent = 46.5 ft / tan (13.1)

This will give us the horizontal distance from the press box to second base.

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