A surveyor is 130 feet from a tower. The angle of elevation to the top of the tower is 32 degrees. Find the height
81.2 feet?
tan32 = height/130
yes
meow
To find the height of the tower, we can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the tower, and the adjacent side is the distance from the surveyor to the tower.
We can set up the equation: tan(angle) = height/distance
Plugging in the values we have: tan(32 degrees) = height/130 feet
To solve for the height, we can rearrange the equation as follows:
height = tan(32 degrees) * 130 feet
Using a calculator, the tangent of 32 degrees is approximately 0.62487. Multiplying this by 130 feet, we find:
height ≈ 0.62487 * 130 feet ≈ 81.2361 feet
Therefore, the height of the tower is approximately 81.2 feet.