Right Triangle Trigonometry
Sine, cosine and tangent relate angles to side ratios.
About this topic
Trigonometry links the angles of a right triangle to the ratios of its sides. For an acute angle θ: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent, remembered as SOH-CAH-TOA. These ratios depend only on the angle, not the triangle's size, because all right triangles with the same acute angle are similar. That is why a single calculator button can serve every triangle ever drawn.
To use the ratios, first label the sides relative to the angle you care about: the hypotenuse is always opposite the right angle, the opposite side faces θ, and the adjacent side touches θ. Switching to the other acute angle swaps the opposite and adjacent labels. The reciprocals csc, sec and cot are 1/sin, 1/cos and 1/tan.
Example: a ladder leans against a wall making a 70° angle with the ground, and its base is 2 m from the wall. Since cos 70° = adjacent/hypotenuse, the ladder length is 2 / cos 70°, about 5.85 m. Surveyors, architects, pilots and game programmers all rely on exactly this kind of calculation.
Common mistakes include forgetting that the calculator must be in degree mode (or radian mode) to match the problem, and mislabeling opposite and adjacent. Always sketch the triangle first and write which ratio connects the known and unknown quantities.
Key ideas
- SOH CAH TOA
- sin = opposite/hypotenuse
- The ratios depend only on the angle
Quick check
Use cases: where Right Triangle Trigonometry helps
- Homework: review the key idea behind Right Triangle Trigonometry before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Right Triangle Trigonometry without notes.
- Visual learning: play with the interactive lab to see how Right Triangle Trigonometry changes when you adjust its inputs.
- Teaching a friend: explain Right Triangle Trigonometry 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 Right Triangle Trigonometry?
Sine, cosine and tangent relate angles to side ratios.
What will I learn in Right Triangle Trigonometry?
SOH CAH TOA. sin = opposite/hypotenuse. The ratios depend only on the angle.
Is Right Triangle Trigonometry 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 Right Triangle Trigonometry 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 Right Triangle Trigonometry?
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.