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From the observation deck of a skyscraper, Dominic measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 984 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.

Respuesta :

The horizontal distance from the base of the skyscraper is 984 feet.

What is height and distance application?

A study on the uses of trigonometry is called Heights and Distances. It can be used in many real-world situations to measure things like an object's height, depth, or the separation between two heavenly objects, among other things.

Given that,

Height of deck h = 984 feet,

Angle of depression θ= 45°

Let horizontal distance is x,

To find horizontal distance of base, use height and distance formula,

tanθ = h/x

Substitute, the values of h and θ,

tan45 = 984/x

∵tan45 = 1

1 = 984/x

⇒x = 984 feet

The horizontal distance from the base of the skyscraper is 984 feet.

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