Finding all trigonometric ratios from one: Class 10 practice
In a right triangle, sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Pythagoras theorem
The idea behind finding all trigonometric ratios from one
In a right triangle, sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. Given one ratio, draw the triangle and use Pythagoras to find the missing side.
Step-by-step method
- Draw a right triangle with the given ratio's sides.
- Use Pythagoras for the third side.
- Write the other ratios.
- Check sin² + cos² = 1.
Worked example 1 (Basic)
If sin A = 7/25, find the other two of sin A, cos A and tan A.
- Take opposite = 7, adjacent = 24, hypotenuse = 25
- Check: 7² + 24² = 625 = 25²
- sin A = 7/25, cos A = 24/25, tan A = 7/24
- Answer: sin A = 7/25, cos A = 24/25, tan A = 7/24
Worked example 2 (Standard)
If cos A = 21/29, find the other two of sin A, cos A and tan A.
- Take opposite = 20, adjacent = 21, hypotenuse = 29
- Check: 20² + 21² = 841 = 29²
- sin A = 20/29, cos A = 21/29, tan A = 20/21
- Answer: sin A = 20/29, cos A = 21/29, tan A = 20/21
Worked example 3 (Challenge)
If tan A = 8/15, find the other two of sin A, cos A and tan A.
- Take opposite = 8, adjacent = 15, hypotenuse = 17
- Check: 8² + 15² = 289 = 17²
- sin A = 8/17, cos A = 15/17, tan A = 8/15
- Answer: sin A = 8/17, cos A = 15/17, tan A = 8/15
Common mistakes and misconceptions
- Mixing up opposite and adjacent
- Writing tan = adjacent/opposite
Practice questions
- (Basic) If sin A = 20/29, find the other two of sin A, cos A and tan A.
- (Basic) If sin A = 3/5, find the other two of sin A, cos A and tan A.
- (Standard) If cos A = 12/13, find the other two of sin A, cos A and tan A.
- (Standard) If cos A = 4/5, find the other two of sin A, cos A and tan A.
- (Challenge) If tan A = 7/24, find the other two of sin A, cos A and tan A.
- (Challenge) If tan A = 3/4, find the other two of sin A, cos A and tan A.
Answer key with full working
- Q1: Take opposite = 20, adjacent = 21, hypotenuse = 29 → Check: 20² + 21² = 841 = 29² → sin A = 20/29, cos A = 21/29, tan A = 20/21 → Answer: sin A = 20/29, cos A = 21/29, tan A = 20/21
- Q2: Take opposite = 3, adjacent = 4, hypotenuse = 5 → Check: 3² + 4² = 25 = 5² → sin A = 3/5, cos A = 4/5, tan A = 3/4 → Answer: sin A = 3/5, cos A = 4/5, tan A = 3/4
- Q3: Take opposite = 5, adjacent = 12, hypotenuse = 13 → Check: 5² + 12² = 169 = 13² → sin A = 5/13, cos A = 12/13, tan A = 5/12 → Answer: sin A = 5/13, cos A = 12/13, tan A = 5/12
- Q4: Take opposite = 3, adjacent = 4, hypotenuse = 5 → Check: 3² + 4² = 25 = 5² → sin A = 3/5, cos A = 4/5, tan A = 3/4 → Answer: sin A = 3/5, cos A = 4/5, tan A = 3/4
- Q5: Take opposite = 7, adjacent = 24, hypotenuse = 25 → Check: 7² + 24² = 625 = 25² → sin A = 7/25, cos A = 24/25, tan A = 7/24 → Answer: sin A = 7/25, cos A = 24/25, tan A = 7/24
- Q6: Take opposite = 3, adjacent = 4, hypotenuse = 5 → Check: 3² + 4² = 25 = 5² → sin A = 3/5, cos A = 4/5, tan A = 3/4 → Answer: sin A = 3/5, cos A = 4/5, tan A = 3/4
Syllabus note
This skill is listed under "Introduction to Trigonometry" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is finding all trigonometric ratios from one in?
"Introduction to Trigonometry", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.