From the observation deck of a skyscraper, Rahul measures a 48 degree 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.
Let $x$ be the horizontal distance from the base of the skyscraper to the ship. Since Rahul measures a $48^\circ$ angle of depression to the ship, we form a right triangle with the horizontal distance as the adjacent side and the height of the skyscraper as the opposite side. Therefore, $$\tan 48^\circ = \frac{x}{1093}$$ $$x = 1093\cdot \tan 48^\circ \approx \boxed{856.0}.$$
ok so whats the answer
The horizontal distance from the base of the skyscraper to the ship is approximately 856.0 feet.
dont round
The exact value of the horizontal distance from the base of the skyscraper to the ship is $x = 1093\cdot \tan 48^\circ \approx 856.0182$ feet.
