Trigonometry · JSS 3, SS 1
Trigonometric ratios (SOH CAH TOA)
Find sides and angles in a right-angled triangle.
- sin θ = oppositehypotenuse
- cos θ = adjacenthypotenuse
- tan θ = oppositeadjacent
What the letters mean
- θ
- the angle you are using
- opposite
- the side facing θ
- adjacent
- the side next to θ (not the hypotenuse)
- hypotenuse
- the longest side, facing the right angle
Worked example
In a right-angled triangle, the side opposite θ is 5 cm and the hypotenuse is 10 cm. Find θ.
Step 1: Opposite and hypotenuse → sine
sin θ = 510 = 0.5
Step 2: Inverse sine
θ = sin−1 0.5 = 30°
Final answer: θ = 30°
SOH CAH TOA: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
See it
Play with this picture from the Sine, Cosine and Tangent lesson.
sin 37°opphyp6.02 ÷ 100.6018
cos 37°adjhyp7.99 ÷ 100.7986
tan 37°oppadj6.02 ÷ 7.990.7536
Change the hypotenuse: the sides change, but the ratios for the same θ stay the same.
Angle θ37°
Hyp.10