Geometry

Question Analysis

The main focus of this problem is to use the angle of elevation (the angle at which the crane's arm is inclined with respect to the ground) and the length of the crane's arm (hypotenuse) to determine the height (opposite side) to which the load is lifted, by applying trigonometric concepts.

Key Concept Explanation

1. Angle of Elevation: It is the angle between the horizontal ground level and the line along which the crane's arm extends (in this case, the line of sight from the base of the crane to the lifted load).

2. Trigonometric Functions in Right - Triangles: For an acute angle  in a right - triangle, , , . When we know the hypotenuse and need to find the opposite side, the sine function is appropriate.

Step - by - Step Solution

1. Let the height to which the load is lifted be  feet.

The angle of elevation  and the length of the crane's arm (hypotenuse)  feet.

Using the sine function