Question

the angle of elevation to the top of a building in new york is found to be 3 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. round to the tenths. hint: 1 mile = 5280 feet your answer is feet. question help: video

Explanation:

Step1: Convert distance from miles to feet

Given \(1\) mile \( = 5280\) feet, so \(2\) miles \(=2\times5280 = 10560\) feet.

Step2: Use tangent function

Let \(h\) be the height of the building. We know that \(\tan\theta=\frac{opposite}{adjacent}\). Here \(\theta = 3^{\circ}\) and adjacent side \(=10560\) feet. So \(\tan(3^{\circ})=\frac{h}{10560}\).
Since \(\tan(3^{\circ})\approx0.0524\), then \(h = 10560\times\tan(3^{\circ})\).

Step3: Calculate the height

\(h=10560\times0.0524 = 553.344\approx553.3\)

Answer:

\(553.3\)