A contractor needs to know the height of a building to estimate the cost of a job. From a point 92 feet away from the base of the building, the angle of elevation to the top of the building is found to be 40°32’. Find the height of the building. Round your answer to the hundredths place.
height/92 = tan 40°32'
height = 92tan 40.5333...° = ....
use your calculator
To find the height of the building, we can use trigonometry. We have a right triangle formed by the distance from the base of the building (92 feet), the height of the building (which we want to find), and the angle of elevation (40°32’).
First, we need to convert the angle from degrees and minutes to decimal form. There are 60 minutes in a degree, so we can calculate:
40°32’ = 40 + (32/60) = 40.5333 degrees (rounded to 4 decimal places).
Now, let's use the tangent function to solve for the height of the building. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this case, the height of the building is the opposite side, and the distance from the base of the building is the adjacent side.
Let's define the height of the building as "h". Therefore, the equation becomes:
tan(40.5333) = h / 92
Now solve for "h":
h = 92 * tan(40.5333)
Using a calculator, we can find that the value of tan(40.5333) is approximately 0.8677.
h ≈ 92 * 0.8677
h ≈ 79.86
Therefore, the height of the building is approximately 79.86 feet (rounded to the hundredths place).