A ladder 6m long leans against a vertical wall at an angle 53º to the horizontal. How high up the wall does the ladder reach?

Analyze the question

The ladder, wall and ground form a right-angled triangle:

• Hypotenuse = ladder = 6 m
• Angle between ladder and ground = 53°
• Height reached on the wall = the side opposite the 53° angle

Concept

Since we have the hypotenuse and want the opposite side, use sine:

sin θ = opposite / hypotenuse

Solution

Height = 6 × sin 53°

sin 53° ≈ 0.7986

Height = 6 × 0.7986 ≈ 4.792 m

Check against the options

This matches option C (4.

Tip

Use SOH-CAH-TOA to choose the ratio:

• Sin = Opposite/Hypotenuse (used here)
• Cos = Adjacent/Hypotenuse
• Tan = Opposite/Adjacent

For ladder problems, the height on the wall is usually L sin θ, and the distance of the foot from the wall is L cos θ, when θ is measured from the ground. Make sure your calculator is in degree mode.