SOHCAHTOA — Introduction
Grade 5What SOHCAHTOA means
SOHCAHTOA is a memory aid for the three trigonometric ratios that link sides and angles in right-angled triangles.
sin θ = Opposite ÷ Hypotenuse
cos θ = Adjacent ÷ Hypotenuse
tan θ = Opposite ÷ Adjacent
The hypotenuse is opposite the right angle. The opposite is the side facing the angle θ. The adjacent is the remaining side, next to angle θ.
Label the triangle first
Before touching a calculator, label the three sides relative to the angle you are working with. Opposite, Adjacent, Hypotenuse. Then choose the correct ratio — it is the one that involves the two sides (or the side and angle) you are dealing with.
If you know or want the Opposite and Hypotenuse, use sin. If Adjacent and Hypotenuse, use cos. If Opposite and Adjacent, use tan. Pick the ratio with your two known pieces.
Worked example — finding a side
EXAMPLE
In a right-angled triangle, the hypotenuse is 12 cm and one angle is 35°. Find the side opposite the 35° angle.
sin 35° = Opposite ÷ Hypotenuse. Opposite = 12 × sin 35° = 12 × 0.5736 ≈ 6.88 cm (to 3 s.f.).
