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From the observation deck of a skyscraper, Rahul measures a
48^(@) angle of depression to a ship in the harbor below. If the observation deck is 1093 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.

From the observation deck of a skyscraper, Rahul measures a $48^{\circ}$ angle of depression to a ship in the harbor below. If the observation deck is $1093$ 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.

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Pythagorean theorem

Full solution

Q. From the observation deck of a skyscraper, Rahul measures a

48^{\circ}

angle of depression to a ship in the harbor below. If the observation deck is

1093

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.

Recognize Angle Relationship: Recognize that the angle of depression is equal to the angle of elevation from the base to the observation deck.
Use Tangent Formula: Use the tangent of the angle of elevation (which is the same as the angle of depression, $48$ degrees) to find the horizontal distance ( $x$ ). $\newline$ $\tan(48^{\circ}) = \frac{\text{opposite}}{\text{adjacent}} = \frac{1093}{x}$
Rearrange Equation: Rearrange the equation to solve for $x$ . $x = \frac{1093}{\tan(48^\circ)}$
Calculate Horizontal Distance: Calculate the horizontal distance using a calculator. $\newline$ $x \approx \frac{1093}{\tan(48)} \approx \frac{1093}{1.1106} \approx 984.8$
Round to Nearest Tenth: Round the answer to the nearest tenth. $x \approx 984.8$ feet

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