Question

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

Answer 1

Answer:

The height of the bullding is 717 ft

Step-by-step 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:

$\displaystyle \tan 82^\circ=\frac{h}{100}$

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