SOLUTION: From the observation deck of a skyscraper, Dominic measures a 45^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 984 feet high, what

Question 1201203: From the observation deck of a skyscraper, Dominic measures a 45^{\circ}
∘
angle of depression to a ship in the harbor below. If the observation deck is 984 feet high, what is the horizontal distance from the base of the skyscraper out to the ship?
Found 3 solutions by Theo, mananth, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
45 degree angle of depressison forms a triangle with a vertical leg of 984 feet in length.
A is the observation deck of the skyscraper.
B is the base of the skyscraper.
C is the location of the ship in the harbor.
angle A is 45 degrees.
ancle C is 45 degrees.
angle B is 90 degrees.
tangent of angle A is equal to opposite side divided by adjacent side is equal to BC / AB
AB is equal to 984 feet and angle A is equal to 45 degrees, therefore:
tangent of 45 degrees is equal to opposite side divided by adjacent side = BC / 984.
solve for BC to get:
BC = 984 * tangent of 45 degrees = 984 feet.
your solution is that the horizontal distance from the base of the skyscraper to the ship is 984 feet.

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
.
distamce is same as that of height of deck

Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!

Since the angle of depression is 45 degrees, the triangle formed by the tower, the horizontal distance to the ship, and the line of sight is an isosceles right triangle, so the distance to the ship is the same as the height of the tower.

ANSWER: 984 feet

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