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From the observation deck of a skyscraper, Bentley measures a
48^(@) angle of depression to a ship in the harbor below. If the observation deck is 969 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.

Question $\newline$ Show Examples $\newline$ From the observation deck of a skyscraper, Bentley measures a $48^{\circ}$ angle of depression to a ship in the harbor below. If the observation deck is $969$ 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. Question

\newline

Show Examples

\newline

From the observation deck of a skyscraper, Bentley measures a

48^{\circ}

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

969

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.

Triangle Description: We got a right triangle with the skyscraper and the ground. The angle of depression is the same as the angle of elevation from the base to the observation deck, which is $48$ degrees.
Observation Deck Height: The height of the observation deck is the opposite side of the triangle, which is $969$ feet.
Calculate Adjacent Side: We need to find the adjacent side, which is the horizontal distance to the ship. We'll use the tangent of the angle, which is opposite over adjacent.
Use Tangent Formula: So, $\tan(48^\circ) = \frac{969}{\text{horizontal distance}}$ .
Solve for Horizontal Distance: Rearrange to solve for the horizontal distance: $\text{horizontal distance} = \frac{969}{\tan(48^\circ)}$ .
Plug in Values: Plug in the values and calculate: horizontal distance $= \frac{969}{\tan(48)}$ .
Calculate Tangent: Use a calculator to find $\tan(48^\circ)$ and divide $969$ by that number.
Final Horizontal Distance: After calculating, we get horizontal distance $\approx \frac{969}{1.1106} \approx 872.7$ feet.

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