The angle of elevation from a buoy to the top of a bridge is 19 degrees. The bridge is 150 feet high. How far from the foot of the bridge's pillar is the buoy?

150/X = tan 19 = 0.3443

Solve for X

To find the distance from the foot of the bridge's pillar to the buoy, we can use trigonometry and the given information.

Let's assume that the distance from the foot of the bridge's pillar to the buoy is represented by 'x'.

We are given that the angle of elevation from the buoy to the top of the bridge is 19 degrees. This means that if we imagine a right triangle formed by the buoy, the base of the triangle (x), and the height of the bridge (150 feet), the angle opposite to the height of the bridge is 19 degrees.

Using trigonometry, specifically the tangent function, we can set up the following equation:

tan(19 degrees) = height of the bridge (150 feet) / distance from the foot of the bridge's pillar (x)

To solve for x, we rearrange the equation:

x = height of the bridge (150 feet) / tan(19 degrees)

Using a calculator, we can evaluate the tangent of 19 degrees and divide the height of the bridge by that value:

x = 150 feet / tan(19 degrees)

x ≈ 422.70 feet

Therefore, the buoy is approximately 422.70 feet from the foot of the bridge's pillar.