Question

The angle of elevation to the top of a very tall Building is found to be 6° from the ground at a distance of 1 mi from the base of the building. Using this information, find the height of the building. (Round your answer to the nearest foot.)

Answer 1

Answer:

555

Explanation:

The scenario is shown in the image attached below. A Right Angled Triangle is formed. We have an angle of 6 degrees, the side adjacent to angle which measures 1 mile and we need to find the side opposite to the angle.

Since 1 mile = 5280 feet, the side adjacent to the angle has a measure of 5280 feet.

Tangent ratio relates the opposite and adjacent side by following formula:

$tan(\theta)=\frac{Opposite}{Adjacent}$

Using the given values, we get:

$tan(6)=\frac{x}{5280}\\\\ x=tan(6) \times 5280\\\\ x = 555$

Thus, rounded to nearest foot, the height of the building is 555 feet