Question

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.

Explanation:

Step1: Define trigonometric relationship

The angle of depression equals the angle of elevation from the ship to the deck, so we use $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 67^\circ$, opposite side $= 883$ ft, adjacent side $= x$ (horizontal distance).
$\tan(67^\circ) = \frac{883}{x}$

Step2: Rearrange to solve for x

Isolate $x$ by cross-multiplying.
$x = \frac{883}{\tan(67^\circ)}$

Step3: Calculate the value

Use $\tan(67^\circ) \approx 2.3559$ to compute $x$.
$x \approx \frac{883}{2.3559} \approx 375$

Answer:

375 feet