Question

from the observation deck of a skyscraper, marques measures a 67° angle of depression to a ship in the harbor below. if the observation deck is 1049 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 2 feet submit answer

Explanation:

Step1: Use the tangent function

The angle of depression is \(67^{\circ}\). The height of the observation deck (opposite side) is \(1049\) feet and the horizontal distance \(x\) (adjacent side) is what we need to find. The tangent of an angle in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Since the angle of depression is equal to the angle of elevation from the ship to the observation deck, \(\tan(67^{\circ})=\frac{1049}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x = \frac{1049}{\tan(67^{\circ})}\). We know that \(\tan(67^{\circ})\approx2.3559\). Then \(x=\frac{1049}{2.3559}\).

Step3: Calculate the value of \(x\)

\(x=\frac{1049}{2.3559}\approx445.3\)

Answer:

\(445.3\)