Question

from the observation deck of a skyscraper, jack measures a 48° angle of depression to a ship in the harbor below. if the observation deck is 1181 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? round your answer to the nearest hundredth of a foot if necessary.

Explanation:

Step1: Relate angle of depression to triangle angle

The angle of depression equals the angle at the ship, so it's $48^\circ$.

Step2: Set up tangent ratio

$\tan(48^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{1181}{x}$

Step3: Solve for x

$x = \frac{1181}{\tan(48^\circ)}$

Step4: Calculate the value

$\tan(48^\circ) \approx 1.1106$, so $x \approx \frac{1181}{1.1106} \approx 1063.39$

Answer:

1063.39