Question

A surveyor is 305 ft from the base of the new courthouse. Her angle-measuring device is 5 ft above the ground. The angle of elevation to the top of the courthouse is 42?. Find the height of the courthouse to the nearest foot.

Answer 1

Answer:

279.62 feet

Step-by-step explanation:

We have a rectangle with 5ft x 305ft sides representing the area between your device and the base of the courthouse.

In addition to this we have an angle of 42 °

The height would come being the length of the opposite side of this triangle.

We know that:

tan (° A) = opposite / adjacent

Adjacent side is 305 ft and ° A is 42 °

Solved for opposite:

Opposite = adjacent * tan (° A)

Opposite = 305 * tan (42) = 274.62 feet

We must add 5 feet to this result and we are left with:

274.62 + 5 = 279.62

It means that the height is 279.62 feet