Question

Ms. Mwanted to estimate the height of the Republic Plaza building in downtown Denver. She has an app on

her phone that will measure an angle of elevation. She determined she was 100 feet from the base of the
building. She held her phone (with the app) at eye level (about 5 feet off the ground) and measured the angle
of elevation to the top of the building to be 82°. What is the height of the building to the nearest foot?

Answer 1

The height of the bullding is 717 ft

Explanation:

Right Triangles

The trigonometric ratios (sine, cosine, tangent, etc.) are defined as relations between the triangle's side lengths.

The tangent ratio for an internal angle A is:

`\displaystyle \tan A=\frac{\text{opposite leg}}{\text{adjacent leg}}`

The image below shows the situation where Ms. M wanted to estimate the height of the Republic Plaza building in downtown Denver.

The angle A is given by his phone's app as A= 82° and the distance from her location and the building is 100 ft. The angle formed by the building and the ground is 90°, thus the tangent ratio must be satisfied. The distance h is the opposite leg to angle A and 100 ft is the adjacent leg, thus:

`\displaystyle \tan 82^\circ=(h)/(100)`

Solving for h:

`h = 100\tan 82^\circ`

Computing:

h = 711.5 ft

We must add the height of Ms, M's eyes. The height of the building is

711.5 ft + 5 ft = 716.5 ft

The height of the building is 717 ft