Question

The angle of elevation to the top of a tall building is found to be 9° from the ground at a distance of 5299 feet from the base of the building. Using this information, find the height of the building.

a) 5299 feet
b) 5299 * tan(9°) feet
c) 5299 * sin(9°) feet
d) None of these

Answer 1

The height of the building can be calculated by multiplying the distance from the base of the building by the tangent of the angle of elevation, which gives 5299 × tan(9°) feet.

Step-by-step explanation:

The student is trying to find the height of the building given the angle of elevation and the distance from the base of the building. In trigonometry, the tangent of an angle in a right triangle is the ratio of the opposite side (height of the building, in this case) to the adjacent side (distance from the base, in this case).

Therefore, the correct approach to finding the height of the building is to use the tangent function (tan) of the given angle of elevation, which is 9°.

Using the formula: height = distance × tan(angle), we can calculate the height as 5299 feet × tan(9°).

The answer therefore is option b) 5299 × tan(9°) feet.