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.
angle =64
adjecent=100
To find the height of the building, we can use the tangent function.
The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this case, the angle is 64 degrees and the adjacent side is 100 units.
Therefore, we can calculate the height of the building using the equation:
tan(angle) = opposite/adjacent
tan(64) = opposite/100
To solve for the opposite side (height of the building), we can multiply both sides of the equation by 100:
100 * tan(64) = opposite
Using a calculator, we can evaluate the tangent of 64 degrees:
100 * tan(64) ≈ 206.96
Therefore, the height of the building is approximately 206.96 units.