Label the opposite, adjacent and hypotenuse from an angle, choose sin, cos or tan, and find a missing side.
What you will learn
- Label the opposite, adjacent and hypotenuse
- Choose the right ratio from the two sides involved
- Find a side with sin, cos or tan
- Find the hypotenuse by dividing
Name the sides from the angle
Mark the angle you are using, θ.
Then:
Not drawn accurately
The hypotenuse is opposite the right angle. The opposite is across the triangle from θ. The adjacent is next to θ and is not the hypotenuse.
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
The first letters spell SOH CAH TOA.
Each ratio is just a fraction of two sides. In a triangle with opposite 8, adjacent 15 and hypotenuse 17 (from θ): sin θ = 8/17, cos θ = 15/17 and tan θ = 8/15. Simplify the fraction if you can: sides 10, 24, 26 give sin θ = 10/26 = 5/13.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Name the sides from the angle
- Find a side in three steps
- Degrees, not radians
- Try it: Sin and cos on the unit circle
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Hypotenuse, Opposite, Adjacent
In this unit: Pythagoras and trigonometry
Pythagoras' theorem, sin, cos and tan in right-angled triangles, angles of elevation, depression and bearings, exact values, 3D problems, and the sine and cosine rules.
- Pythagoras' theorem
- Sin, cos and tan for sides
- Finding angles, elevation and bearings
- Exact values and 3D
- The sine and cosine rules