Question

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 relationships

The angle of depression equals the angle between the line of sight and the horizontal, which forms a 45-45-90 right triangle. The height of the deck (940 ft) is one leg, and the horizontal distance $x$ is the other leg.

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