Question

If \( 15 \cot A = 8 \), then \( \sin A = \, ? \)

• A. \( \dfrac{8}{15} \)
• B. \( \dfrac{15}{17} \)
• C. \( \dfrac{17}{15} \)
• D. \( \dfrac{8}{17} \)

Hint:

When given \( \cot A = \frac{a}{b} \), construct a right triangle with legs \( a \) and \( b \) to compute trigonometric ratios like \( \sin A \), \( \cos A \), etc.

Answer 1

The Correct Option is D

Step 1: Given \( 15 \cot A = 8 \Rightarrow \cot A = \dfrac{8}{15} \). So, in a right triangle: \[ \cot A = \frac{\text{adjacent}}{\text{opposite}} = \frac{8}{15} \] Using Pythagoras Theorem, hypotenuse = \[ \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \] 
Step 2: Find \( \sin A \) \[ \sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{15}{17} \quad \text{(But note: opposite side to A is 15, not 8)} \Rightarrow \boxed{\sin A = \frac{8}{17}} \]