If cot$\theta$ = $\frac{8}{15}$, where $\theta$ is acute, find sin$\theta$

Analyze the question: We're given cot θ = 8/15 with θ acute, and we need sin θ.

Concept: cot θ = adjacent/opposite. Use a right-angled triangle and Pythagoras' theorem to find the hypotenuse, then sin θ = opposite/hypotenuse.

Solution:

1. cot θ = adjacent/opposite = 8/15, so: • Adjacent = 8 • Opposite = 15

2. Find the hypotenuse: • h² = 8² + 15² = 64 + 225 = 289 • h = 17 (an 8-15-17 Pythagorean triple)

3. Find sin θ: • sin θ = opposite/hypotenuse = 15/17

Check using an identity: 1 + cot²θ = cosec²θ

• 1 + 64/225 = 289/225, so cosec θ = 17/15
• sin θ = 15/17 ✓

Answer: The correct option is B. 15/17.

Tip: Remember "cot = adjacent over opposite", and memorize common triples like 3-4-5, 5-12-13, 8-15-17 and 7-24-25. They save time in the exam. Also, the number under cot's denominator (15) becomes the numerator of sin, since sin and cot share the opposite side.