Trigonometry · Grades 10 to 12
Right triangle trigonometry
Use sine, cosine and tangent on right triangles.
The idea
SOH CAH TOA names the three ratios in a right triangle: sine = opposite / hypotenuse, cosine = adjacent / hypotenuse, tangent = opposite / adjacent.
To find a side, multiply the hypotenuse or leg by the ratio. To find an angle, use the inverse ratio.
Worked examples
- How to Find a Missing Side with Sine Find the opposite side when the angle is 30 degrees and the hypotenuse is 12. Four steps with SOH CAH TOA and the mistakes to avoid.
- How to Find a Missing Angle with Cosine Find the angle when cos theta is 1/2. Three steps with the inverse cosine, the exact answer, and the ratio mistakes to avoid.
- How to Find a Missing Angle with Inverse Sine Solve sin theta = 1/2 for an acute angle. Three steps that use inverse sine and the unit circle, with the wrong-ratio mistakes to avoid.
Practice this topic
4 problems with answers.