Question

5.2 part 2
score: 8/10 answered: 8/10
question 9
the angle of elevation to the top of a building in new york is found to be 5 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: read message instructor

Explanation:

Step1: Convert distance from miles to feet

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

Step2: Use the tangent function

We know that \(\tan\theta=\frac{opposite}{adjacent}\). Here, \(\theta = 5^{\circ}\), the adjacent side \(x = 10560\) feet, and the opposite side \(y\) (height of the building) is what we want to find.
So, \(\tan(5^{\circ})=\frac{y}{10560}\).
Since \(\tan(5^{\circ})\approx0.087488\), then \(y = 10560\times\tan(5^{\circ})\).
\(y=10560\times0.087488\)
\(y = 923.87328\)

Answer:

\(923.9\)