Question

The angle of elevation to the top of a tall building is found to be 8° from the ground at a distance of 1.4 mile from the base of the building. Using this information, find the height of the building.

The buildings height is ? feet.
Report answer accurate to 2 decimal places.

Answer 1

To find the height of the building, we can use trigonometry. We have the angle of elevation (8°) and the distance from the base of the building to the observation point (1.4 miles).

Let's convert the distance from miles to feet:
1 mile = 5280 feet
1.4 miles = 1.4 * 5280 feet = 7392 feet

Now, we can set up a right triangle with the height of the building as the opposite side, the distance to the building as the adjacent side, and the angle of elevation as the angle. Using the tangent function:

tan(angle) = opposite/adjacent

tan(8°) = height/7392

To find the height, we can rearrange the equation:

height = tan(8°) * 7392

Calculating the value:

height ≈ 0.1405 * 7392

height ≈ 1039.52 feet

Therefore, the height of the building is approximately 1039.52 feet.