Question

question 15 of 25
the angle of elevation to the top of a 15 - story skyscraper is measured to be 4
from a point on the ground 2500 feet from the building. what is the height
of the skyscraper to the nearest hundredth of a foot?
a. 174.39 feet
b. 83.13 feet
c. 96.49 feet
d. 174.82 feet

Explanation:

Step1: Define variables

Let height = \( h \), distance = 2500 ft, angle = \( 4^\circ \) (assumed, as image cuts off but options fit).

Step2: Use tangent function

\( \tan(\theta) = \frac{h}{\text{distance}} \) → \( h = 2500 \times \tan(4^\circ) \)

Step3: Calculate value

\( \tan(4^\circ) \approx 0.0699268119 \), so \( h \approx 2500 \times 0.0699268119 \approx 174.817 \)

Step4: Round to nearest hundredth

\( h \approx 174.82 \)

Answer:

D. 174.82 feet