Question

from the observation deck of a skyscraper, aaliyah measures a 67° angle of depression to a ship in the harbor below. if the observation deck is 883 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. answer attempt 1 out of 3

Explanation:

Step1: Use the tangent function

The angle of depression is \(67^{\circ}\). The vertical side (height of the observation deck) is \(883\) feet, and the horizontal side is \(x\). The tangent of an angle in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\tan(67^{\circ})=\frac{883}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x = \frac{883}{\tan(67^{\circ})}\). We know that \(\tan(67^{\circ})\approx2.355852366\). Then \(x=\frac{883}{2.355852366}\).

Answer:

\(x\approx375.7\) feet