Solving Right Triangles
Use trig ratios and inverses to find sides and angles.
About this topic
To solve a right triangle means finding all missing sides and angles. Use the Pythagorean theorem for a missing side when two are known, the trig ratios when you have an angle and a side, and inverse functions (sin⁻¹, cos⁻¹, tan⁻¹) to find angles from side ratios. The two acute angles always add to 90°, which gives the last angle for free.
A good strategy is to decide what you know and pick the single tool that links it to what you want. With two sides known, find an angle using an inverse trig function and then the remaining side using Pythagoras. With one side and one acute angle known, subtract from 90° to get the other angle and use sine, cosine or tangent for the other sides.
Example: a right triangle has hypotenuse 10 and one leg 6. The other leg is the square root of 100 − 36 = 8. The angle opposite the leg 6 is sin⁻¹(6/10), about 36.9°, and the other acute angle is about 53.1°.
Engineers use this to compute the length of a ramp, the height of a tower or the slope of a roof. Tips: keep full precision until the final step to avoid rounding drift, check that the longest side is the hypotenuse, and confirm that your answers are reasonable by seeing that bigger angles face bigger sides.
Key ideas
- Pick the ratio that has your known and unknown
- Use sin⁻¹, cos⁻¹, tan⁻¹ for angles
- Check with the Pythagorean theorem
Quick check
Use cases: where Solving Right Triangles helps
- Homework: review the key idea behind Solving Right Triangles before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Solving Right Triangles without notes.
- Visual learning: play with the interactive lab to see how Solving Right Triangles changes when you adjust its inputs.
- Teaching a friend: explain Solving Right Triangles in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Solving Right Triangles?
Use trig ratios and inverses to find sides and angles.
What will I learn in Solving Right Triangles?
Pick the ratio that has your known and unknown. Use sin⁻¹, cos⁻¹, tan⁻¹ for angles. Check with the Pythagorean theorem.
Is Solving Right Triangles part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Solving Right Triangles lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Solving Right Triangles?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.