EXAMPLE 2 A ladder 10 m long leans against a wall. The angle between the ladder and the ground is 30°. Find the height reached on the wall.

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

• The length of the ladder is the hypotenuse (H) = 10 m.
• The angle between the ladder and the ground is θ = 30°.
• The height reached on the wall is the side opposite (O) to the angle θ.

We know the hypotenuse and the angle, and we want to find the opposite side. The sine function relates these three:
sin(θ) = Opposite / Hypotenuse

sin(30°) = Height / 10 m
We know that sin(30°) = 0.5.

0.5 = Height / 10 m
Height = 0.5 × 10 m
Height = 5 m

The height reached on the wall is 5 m.