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From the observation deck of a skyscraper, Lavaughn measures a 42°
angle of depression to a ship in the harbor below. If the observation deck is 872 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

Respuesta :

facundo3141592

By using trigonometry, we conclude that the horizontal distance is 785.15ft

How to find the horizontal distance?

We can think of this as a right triangle.

Where the height of the observation deck is one cathetus and the horizontal distance is the other cathetus,

We know that the depression angle when looking from above is 42°. If we step on this angle, the adjacent cathetus is the height of the deck, then the horizontal distance is the opposite cathetus.

Then we can use the relation:

tan(a) = (opposite cathteus)/(adjacent cathetus).

Replacing what we know:

tan(42°) = (distance)/(872ft)

tan(42°)*872ft = distance = 785.15ft

The horizontal distance is 785.15ft

If you want to learn more about right triangles:

https://brainly.com/question/2217700

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