Question

1. -/1 points details my notes ask your teacher practice another there is an antenna on the top of a building. from a location 500 feet from the base of the building, the angle of elevation to the top of the building is measured to be 35°. from the same location, the angle of elevation to the top of the antenna is measured to be 39°. find the height of the antenna. (round your answer to three decimal places.) ft the angle of elevation to the top of a building in a city 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 your answer to four decimal places.) ft

Explanation:

Step1: Convert miles to feet

We know that 1 mile = 5280 feet, so 2 miles = 2×5280 = 10560 feet.

Step2: Use tangent function

Let the height of the building be $h$. In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 3$ degrees and the adjacent side to the angle of elevation is the distance from the base of the building, which is 10560 feet. So $\tan(3^{\circ})=\frac{h}{10560}$.

Step3: Solve for $h$

We know that $\tan(3^{\circ})\approx0.0524$, then $h = 10560\times\tan(3^{\circ})\approx10560\times0.0524 = 553.344$ feet.

Answer:

553.344 feet