Geometry

Question Analysis

The main focus of this problem is to use the length of the ladder (hypotenuse) and the angle it makes with the ground (angle of elevation) to find the height on the wall that the ladder reaches (opposite side) by applying trigonometric functions.

 

Key Concept Explanation

1. Angle of Elevation: In this context, it is the angle between the ground and the ladder, which helps in establishing relationships between the sides of the right - triangle formed by the ladder, the wall, and the ground.

2. Trigonometric Functions in Right - Triangles: For an acute angle  in a right - triangle, , , . Given the hypotenuse (length of the ladder) and needing to find the opposite side (height on the wall), the sine function is appropriate.

 

Step - by - Step Solution

1. Let the height on the wall that the ladder reaches be  meters.

The length of the ladder (hypotenuse)  meters and the angle of elevation .

Using the sine function , we substitute the values:

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