Question

If $tan\theta=\frac{3}{4}$ and θ is acute, then what is the value of sin θ

• A. $$\frac{-3}{5}$$
• B. $$\frac{3}{5}$$
• C. $$\frac{4}{5}$$
• D. $$\frac{-4}{5}$$

Answer 1

Answer:

$$\frac{3}{5}$$

Solution:

Given:

$tan\theta=\frac{3}{4}$

Formula used:

tanθ = Perpendicular/Base

sinθ = Perpendicular/Hypotenuse

By Pythagoras' theorem,

H² = P² + B²

Calculation:

tan θ = Perpendicular/Base $=\frac{3}{4}$

So, by Pythagoras' theorem,

H2 = P2 + B²

⇒ H² = 3² + 4²

⇒ H² = (9 + 16)

⇒ H² = 25

⇒ H = 5 cm

⇒ sin θ = Perpendicular/Hypotenuse $=\frac{3}{5}$

∴ The required value is $\frac{3}{5}$.