Geometry

Question Analysis

This question involves Elevation and Depression Angles. The main focus is on using trigonometry to find the angle of elevation when the height of an object (the skyscraper) and the horizontal distance from the observer to the object are given.

Key Concept Explanation

We use the tangent function in a right - triangle. In a right - triangle formed by the skyscraper (vertical side), the horizontal distance from the base of the building to the viewing point (adjacent side), and the line of sight from the viewing point to the top of the building, the tangent of the angle of elevation is defined as the ratio of the length of the opposite side (height of the building) to the length of the adjacent side (horizontal distance).

Step - by - Step Solution

Let the angle of elevation be . The height of the skyscraper (opposite side)  feet and the horizontal distance (adjacent side)  feet.

We know that .

Substituting the given values,