Ladder Height Calculation Using Trigonometry

This problem involves a right-angled triangle formed by the ladder, the wall, and the ground. We are given the ladder's length (hypotenuse) and the angle it makes with the ground. We need to find the height it reaches on the wall (opposite side).

Identify Given Information

• Ladder Length (Hypotenuse): $L = 28$ m
• Angle with Ground: $\theta = 60°$
• Goal: Find the height on the wall (Opposite Side): $h$

Apply Trigonometric Relation

The sine function connects the angle, the opposite side (height), and the hypotenuse (ladder length):

$ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} $

Substitute the known values:

$ \sin(60°) = \frac{h}{28} $

Solve for Height (h)

Rearrange the equation to find '$h$':

$ h = 28 \times \sin(60°) $

Recall that $\sin(60°) = \frac{\sqrt{3}}{2}$.

$ h = 28 \times \frac{\sqrt{3}}{2} $

Simplify:

$ h = 14 \times \sqrt{3} $

Calculate the Final Value

Use the given approximation $\sqrt{3} \approx 1.74$:

$ h = 14 \times 1.74 $

$ h = 24.36 \text{ m} $

Result

The height at which the ladder touches the wall is 24.36 m.