Question

from the observation deck of a skyscraper, brandon measures a 45° angle of depression to a ship in the harbor below. if the observation deck is 1140 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

Let the horizontal distance be \(x\). The angle of depression is \(45^{\circ}\), and the height of the observation deck (opposite side) is \(h = 1140\) feet. Since the angle of depression is equal to the angle of elevation from the ship to the observation deck. We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 45^{\circ}\), opposite side \(= 1140\) and adjacent side \(=x\). So, \(\tan(45^{\circ})=\frac{1140}{x}\).

Step2: Solve for \(x\)

Since \(\tan(45^{\circ}) = 1\), we have the equation \(1=\frac{1140}{x}\). Cross - multiplying gives \(x = 1140\) feet.

Answer:

\(1140.0\) feet