Advanced · 15 min
Right-triangle trigonometry
Choose sine, cosine, or tangent from the sides involved.
Name sides relative to an angle
The hypotenuse is opposite the right angle. Relative to the chosen acute angle, sine is opposite divided by hypotenuse and cosine is adjacent divided by hypotenuse.
Worked example
For opposite side 3, adjacent side 4, and hypotenuse 5: sin θ = 3/5 and cos θ = 4/5.
Choose a ratio to find a side
Tangent is opposite divided by adjacent. Use the ratio containing the known and required sides. Degree-based angles need a calculator in degree mode.
Worked example
At θ = 45°, tan θ = 1, so the opposite and adjacent sides are equal.
Choose the correct ratio
- Draw a right triangle and label a chosen acute angle, its opposite side, its adjacent side, and the hypotenuse.
- Write the three trigonometric ratios using your side labels.