Question

The angle of elevation to the top of a particular skyscraper in New York is found to be 12 degrees from the ground at a distance of 1.3 mi from the base of the building. Using this information, find the height of the skyscraper. * 20 points a. 1560 ft b. 2918 ft c. 1459 ft

Answer 1

Answer:

The height of the skyscraper is 1,459 ft. Choice c

Step-by-step explanation:

Right Triangles

The ground and the building form a right angle (90°). In the right triangles, the trigonometric ratios are satisfied. To solve the problem we use the tangent ratio, defined as:

$\displaystyle \tan\theta=\frac{\text{opposite side}}{\text{adjacent side}}$

The angle of elevation from which the skyscraper can be seen is θ=12°. The opposite side of this angle is the height of the skyscraper H and the adjacent side is the distance from the ground X=1.3 miles.

Converting miles to feet: X=1.3*5,280 = 6,864 ft

Applying the tangent ratio to the angle of elevation:

$\displaystyle \tan 12^\circ=\frac{H}{6,864}$

Solving for H:

$H=6,864\tan 12^\circ$

Calculating:

H = 1,459 ft

The height of the skyscraper is 1,459 ft. Choice c