If 24 cot θ = 7, then sin θ is equal to:

1. $\Big(\dfrac{24}{7}\Big)$

2. $\Big(\dfrac{24}{25}\Big)$

3. $\Big(\dfrac{7}{25}\Big)$

4. $\Big(\dfrac{25}{24}\Big)$

Given,

24 cot θ = 7

cot θ = $\dfrac{7}{24} = \dfrac{\text{adjacent}}{\text{opposite}}$

We know that,

$\Rightarrow \text{Hypotenuse} = \sqrt{\text{opposite}^2 + \text{adjacent}^2 } \\[1em] = \sqrt{(24)^2 + (7)^2} \\[1em] = \sqrt{576 + 49} \\[1em] = \sqrt{625} \\[1em] = 25.$

Now,

sin θ = $\dfrac{\text{opposite}}{\text{hypotenuse}} = \dfrac{24}{25}$

Hence, option 2 is the correct option.