The press box at a baseball park is 34ft above the ground. A reporter in the press box looks at an angle of 17 degrees below the horizontal to see second base. What is the horizontal distance from the press box to second base?
34/distance= sinTheta
solve for distance.
tanTheta = h/b
=> b=h/tanTheta
=>b= 34ft/tan(17)
=>b= 111.2ft
111.2ft
To find the horizontal distance from the press box to second base, we can use trigonometry. We know that the height of the press box (opposite side) is 34ft and the angle of depression (17 degrees) from the horizontal line (adjacent side).
First, let's label the sides of the triangle:
- The opposite side (O) is the height of the press box, which is 34ft.
- The adjacent side (A) is the horizontal distance we are trying to find.
- The angle between the horizontal line and the line of sight to second base is 17 degrees.
We can use the tangent function to calculate the horizontal distance (A):
tan(17°) = O/A
Now, let's substitute the values:
tan(17°) = 34ft/A
To solve for A, we can rearrange the equation:
A = 34ft / tan(17°)
Using a calculator, we can find the value of tan(17°) and then calculate the horizontal distance:
A ≈ 114.73ft (rounded to two decimal places)
Therefore, the horizontal distance from the press box to second base is approximately 114.73 feet.