Question

The angle of elevation tot the top of a tall building is found to be 10° from the ground at a distance of 1.3 mile from the base of the building. ​what is the height of the building?

Answer 1

Answer: 0.229 mile = 1210.3 feet

Explanation:

Draw a 90° triangle and label the following (see attachment):

• base angle = 10°
• length of the base = 1.3 mile
• height = x

Since the information given is adjacent to the angle and the information needed is opposite of the angle, we can use tan to solve for the height.

`tan\ \theta=(opposite)/(adjacent)\\\\\\tan\ 10^o=(x)/(1.3)\\\\\\1.3\cdot tan\ 10^o=x\\\\.\qquad 0.229=x`

Since we don't usually measure height of a building in miles, let's convert it to feet (1 mile = 5280 feet)

`0.229\ miles *\ (5280\ feet)/(1\ mile) =1210.3\ feet`