Question

If \( \tan \theta = \frac{3}{4} \), then \( \sin \theta \) is:

• A. \( \frac{4}{5} \)
• B. \( \frac{2}{3} \)
• C. \( \frac{4}{3} \)
• D. \( \frac{3}{5} \)

Hint:

For right-angled triangles, always use Pythagoras theorem to find missing sides.

Answer 1

The Correct Option is D

Using Pythagoras theorem, for \( \tan \theta = \frac{3}{4} \):
\[ \text{Hypotenuse} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] \[ \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{5} \]