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from the observation deck of a skyscraper, jordan measures a $45^\circ$ angle of depression to a ship in the harbor below. if the observation deck is 940 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: Identify right triangle properties

The angle of depression equals the angle of elevation from the ship to the deck, so the triangle has a $45^\circ$ angle, height $940$ ft, and horizontal distance $x$.

Step2: Use tangent of 45°

$\tan(45^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{940}{x}$
Since $\tan(45^\circ) = 1$, substitute:
$1 = \frac{940}{x}$

Step3: Solve for x

Rearrange to isolate $x$:
$x = 940$

Answer:

940.00 feet