Question

from the observation deck of a skyscraper, rahul measures a 48° angle of depression to a ship in the harbor below. if the observation deck is 1093 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? round your answer to the nearest tenth of a foot if necessary.

Explanation:

Step1: Use the tangent function

The angle of depression is \(48^{\circ}\), and the height of the observation deck (opposite side) is \(h = 1093\) feet. Let the horizontal distance (adjacent side) be \(x\). The angle of depression is equal to the angle of elevation from the ship to the observation deck. We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan(48^{\circ})=\frac{1093}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x=\frac{1093}{\tan(48^{\circ})}\). Since \(\tan(48^{\circ})\approx1.1106\), then \(x = \frac{1093}{1.1106}\).

Step3: Calculate the value of \(x\)

\(x=\frac{1093}{1.1106}\approx984.2\)

Answer:

\(984.2\) feet