Right Triangle Trigonometry Basics
A free Geometry lesson from the “Triangles, Similarity, and Trigonometry” unit, with a worked example and practice problems including step-by-step solutions.
Right triangle trigonometry compares side lengths from the viewpoint of an acute angle. Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent. In Triangles, Similarity, and Trigonometry, students need to read the diagram, name the relationship, choose a theorem or formula, and justify why the result follows. The expanded practice now includes fluency, transfer, cumulative review, and proof-style reasoning so Geometry feels connected instead of isolated by topic.
What you'll learn
- Identify opposite, adjacent, and hypotenuse
- Use sine, cosine, and tangent ratios
- Solve simple right-triangle ratio problems
Worked example
Problem. In a right triangle, relative to angle A, the opposite side is 6, adjacent side is 8, and hypotenuse is 10. Find sin A.
- Sine is opposite over hypotenuse.
- sin A = 6/10.
- Simplify to 3/5.
- Connect the result back to Right Triangle Trigonometry Basics so the geometric relationship is explicit.
Answer: 3/5
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. A right triangle has opposite 3 and hypotenuse 5. What is sine?
Show solution
- Sine = opposite/hypotenuse.
Answer: 3/5
2. A right triangle has adjacent 4 and hypotenuse 5. What is cosine?
Show solution
- Cosine = adjacent/hypotenuse.
Answer: 4/5
3. A right triangle has opposite 6 and adjacent 8. What is tangent?
Show solution
- Tangent = opposite/adjacent.
- 6/8 simplifies to 3/4.
Answer: 3/4
4. If sin A = 5/13 and the hypotenuse is 13, what is the opposite side?
Show solution
- Sine is opposite over hypotenuse.
Answer: 5
5. If tan A = 7/24 and the adjacent side is 24, what is the opposite side?
Show solution
- Tangent is opposite over adjacent.
Answer: 7
Practice this interactively with instant feedback and an AI tutor.
Practice Right Triangle Trigonometry Basics Take the free placement check