Question

the angle of elevation to the top of a building in new york is found to be 4 degrees from the ground at a distance of 2 miles from the base of the building. using this information, find the height of the building in feet. (hint: 1 mile = 5280 feet) round answer to one decimal place. your answer is feet.

Explanation:

Step1: Convert miles to feet

Given distance is \(2\) miles. Since \(1\) mile \( = 5280\) feet, then \(2\) miles \(=2\times5280 = 10560\) feet.

Step2: Use tangent function

Let the height of the building be \(h\). We know that \(\tan\theta=\frac{h}{d}\), where \(\theta = 4^{\circ}\) (angle of elevation) and \(d = 10560\) feet (distance from the base). So \(h=d\times\tan\theta\).
Substituting the values, \(h = 10560\times\tan(4^{\circ})\).
We know that \(\tan(4^{\circ})\approx0.06992681\).
Then \(h=10560\times0.06992681\approx738.4\)

Answer:

\(738.4\)