Question

If tan A = 3, then what is the value of 3 sin A cos A?

• A. 8/9
• B. 9/10
• C. 7/9
• D. 9/11

Answer 1

Answer:

B. 9/10

Solution:

Given:

tan A = 3

Concept Used: 

tanθ = Perpendicular/Base

cosθ = Base/Hypotenuse

Pythagoras Theorem

Hypotenuse² = Perpendicular² + Base²

Calculation:

tan A = 3 

⇒ Perpendicular/Base = 3/1

Perpendicular = 3 and Base = 1

Pythagoras Theorem

Hypotenuse² = Perpendicular² + Base²

⇒ Hypotenuse2 = 3² + 1²

⇒ Hypotenuse² = 10

⇒ Hypotenuse = √10

⇒ Cos A = 1/√10

⇒ sin A = 3/√10

⇒ 3 sin A cos A = 3 × 3/√10 × 1/√10

⇒ 9/10

∴ Option B is the correct answer.