This is a typical Class 10 CBSE trigonometry problem. If you’re given tan A = 4/3, the goal is to find the remaining five trigonometric ratios. Let’s solve this step by step using the triangle sides: perpendicular, base, and hypotenuse.
Step-by-Step Solution:
We are given:
- tan A = 4/3
That means: - Perpendicular = 4 units
- Base = 3 units
Now, let’s find the hypotenuse using the Pythagoras Theorem:
Hypotenuse² = Perpendicular² + Base²
Hypotenuse² = 4² + 3² = 16 + 9 = 25
Hypotenuse = √25 = 5
So, the triangle has:
- Perpendicular = 4
- Base = 3
- Hypotenuse = 5
All Trigonometric Ratios of ∠A:
- sin A = Perpendicular / Hypotenuse = 4 / 5
2. cos A = Base / Hypotenuse = 3 / 5
3. tan A = Perpendicular / Base = 4 / 3 (Given)
4. cot A = Base / Perpendicular = 3 / 4
5. sec A = Hypotenuse / Base = 5 / 3
6. cosec A = Hypotenuse / Perpendicular = 5 / 4
Final Answer:
- sin A = 4/5
- cos A = 3/5
- tan A = 4/3
- cot A = 3/4
- sec A = 5/3
- cosec A = 5/4
Why This is Important:
- Helps solve problems related to heights and distances
- Shows how all trigonometric ratios connect through a triangle
- Builds a strong base for advanced math topics in higher classes
Quick Recap:
If tan A = 4/3, draw a triangle where:
- Perpendicular = 4
- Base = 3
Then find the hypotenuse using Pythagoras Theorem and calculate all six trigonometric ratios using the side formulas.
Author: Aman Sir
Aman Sir, the founder of Maths Vidya Institute, has more than 14+ years of experience teaching CBSE Maths to Classes 9–12. His practical explanations help students grasp even the toughest math topics with ease.
