Question

question
from the observation deck of a skyscraper, parker measures a 42° angle of depression to a ship in the harbor below. if the observation deck is 808 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.
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answer attempt 1 out of 2

Explanation:

Step1: Identify trigonometric ratio

The angle of depression is $42^\circ$, which equals the angle of elevation from the ship to the deck. We use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$, so $\tan(42^\circ)=\frac{808}{x}$.

Step2: Rearrange to solve for $x$

Rearrange the formula to isolate $x$: $x=\frac{808}{\tan(42^\circ)}$

Step3: Calculate the value

First, find $\tan(42^\circ)\approx0.9004$. Then compute $x\approx\frac{808}{0.9004}\approx897.38$

Answer:

$897.38$ feet