The students in Mr. Collin's class used a surveyor's measuring device to find the angle from their location to the top of a building. They also measured their distance from the bottom of the building. The diagram shows the angle measure and the distance. To the nearest foot, what is the height of the building?
The lenth of the floor before the building is 100 feet the angle from there location to the top of the building is 64*
Choose from the answers below:
44 ft
205 ft
90 ft
154 ft
To find the height of the building, we can use the tangent function:
tan(angle) = opposite/adjacent
In this case, the angle is 64 degrees and the adjacent side (the distance from the bottom of the building) is 100 feet. Let's denote the height of the building as "h".
tan(64) = h/100
To find h, we can rearrange the equation:
h = tan(64) * 100
Using a calculator, we find:
h ≈ 205 ft
Therefore, the height of the building is approximately 205 ft.