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From the observation deck of a skyscraper, Micaela measures a 45^{\circ}
∘
angle of depression to a ship in the harbor below. If the observation deck is 870 feet high, what is the horizontal distance from the base of the skyscraper out to the ship?

Sagot :

The horizontal distance from the base of the skyscraper to the ship is 870 feet.

Data;

  • Angle of Depression = 45°
  • Observation Deck = 870 feet

Horizontal Distance

To calculate the horizontal distance from the base of the skyscraper, we can use trigonometric ratio SOHCAHTOA here;

Since we have the value of angle and opposite, we can calculate the adjacent using tangent of the angle.

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

Let's substitute the values and solve

[tex]Tan 45 = \frac{870}{x} \\x = \frac{870}{tan 45} \\x = 870 ft[/tex]

The horizontal distance from the base of the skyscraper to the ship is 870 feet.

Learn more on trigonometric ratio here;

https://brainly.com/question/11967894

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