Salvador and Armando use a land surveying tool, a clinometer, to determine the angle of depression from their position on a bridge to a person in a boat on the water. They know the bridge is 110 feet above the water and the angle of depression is 40 degrees. How far (to the nearest foot) horizontally is the boat from Salvador and Armando?
To find the horizontal distance from Salvador and Armando to the boat, we can use trigonometry.
We know that the angle of depression is 40 degrees and the height of the bridge is 110 feet. Let x be the horizontal distance from Salvador and Armando to the boat.
Using the tangent function:
tan(40 degrees) = 110 / x
x = 110 / tan(40 degrees)
x ≈ 110 / 0.8391
x ≈ 131 feet
Therefore, the boat is approximately 131 feet horizontally from Salvador and Armando.