Final answer:
The horizontal distance from the base of the skyscraper to the ship is equal to the height of the observation deck, 870 feet, because the angle of depression measured is 45° which creates an isosceles right triangle with equal height and base lengths.
Step-by-step explanation:
The student's question involves finding the horizontal distance from the base of a skyscraper to a ship at sea when given the height of the observation deck and the angle of depression. We can use trigonometry, specifically the tangent function, which relates angles to the ratio of the opposite side over the adjacent side in a right-angled triangle.
Micaela measures a 45° angle of depression to the ship. This means that inside the triangle formed by the line from Micaela's eyes to the ship, the horizontal distance, and the height of the skyscraper's observation deck, we have a 45° angle at Micaela's observation point. Since opposite and adjacent sides in a 45° triangle are equal, the horizontal distance she is looking for is the same as the height of the observation deck.
Therefore, the horizontal distance from the base of the skyscraper to the ship is 870 feet, which is the height of the observation deck above the harbor. We do not need to do any further calculations in this case because the angle of 45° creates an isosceles right triangle where the height and horizontal distance are equal.