Solve each problem.See Examples 3 and 4. Distance from the Ground to the Top of a Building The angle of depression from the top of a building to a point on the ground is 32°30'. How far is the point on the ground from the top of the building if the building is 252 m high?

Key Concepts

Angle of Depression

The angle of depression is the angle formed by a horizontal line from an observer's eye to an object below the horizontal line. In this context, it helps determine the relationship between the height of the building and the distance to the point on the ground. Understanding this angle is crucial for applying trigonometric functions to solve the problem.

Trigonometric Ratios

Trigonometric ratios, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. In this scenario, the tangent function can be used, as it relates the angle of depression to the opposite side (height of the building) and the adjacent side (distance from the building). Mastery of these ratios is essential for solving problems involving right triangles.

Right Triangle Properties

A right triangle has one angle measuring 90 degrees, and the relationships between its sides and angles are governed by trigonometric principles. In this problem, the height of the building and the distance to the point on the ground form a right triangle with the angle of depression. Recognizing and applying the properties of right triangles is vital for finding the unknown distance.