Geometry

Question Analysis

The main focus of this problem is to use the angle of inclination of the ramp and the horizontal distance along the ramp to find the length of the ramp. We will apply trigonometry in the right - triangle formed by the ramp, the ground, and the vertical height.

Key Concept Explanation

1. Angle of Inclination: It is the angle between the ramp and the ground. In a right - triangle, this angle helps in establishing relationships between the sides of the triangle.

2. Trigonometric Functions in Right - Triangles: For an acute angle  in a right - triangle, , where the adjacent side is the horizontal distance along the ramp and the hypotenuse is the length of the ramp.

Step - by - Step Solution

1. Let the length of the ramp be  meters.

The horizontal distance (adjacent side)  meters and the angle of inclination .

Using the cosine function , we substitute the values:

Click "Show Answer" to reveal the answer and analysis