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From the observation deck of a skyscraper, Harper measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1145 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.

Sagot :

The horizontal distance between the base of the skyscraper to the ship is 1145 feet.

Data;

  • Angle = 45 degree
  • Observation deck (adjacent) = 1145 ft
  • horizontal distance (opposite) = x

Trigonometric Ratios

Using trigonometric ratios, we have the value of adjacent and angle, we can easily use tangent of the angle to find the horizontal distance

[tex]tan\theta = \frac{opposite}{adjacent}[/tex]

Substitute the values into the equation and solve

[tex]tan45 = \frac{x}{1145}\\ x = 1145tan45\\x = 1145ft[/tex]

The horizontal distance between the base of the skyscraper to the ship is 1145 feet.

Learn more on trigonometric ratio here;

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