Question

if cot θ = 5/10, what is sin θ? sin θ =?/√

Explanation:

Step1: Recall cotangent definition

$\cot\theta=\frac{\text{adjacent}}{\text{opposite}}=\frac{5}{10}$. Let the adjacent - side to angle $\theta$ be $a = 5$ and the opposite - side be $b = 10$.

Step2: Use the Pythagorean theorem to find the hypotenuse

By the Pythagorean theorem $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse. So $c=\sqrt{5^{2}+10^{2}}=\sqrt{25 + 100}=\sqrt{125}$.

Step3: Recall sine definition

$\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Since the opposite - side $b = 10$ and the hypotenuse $c=\sqrt{125}$, then $\sin\theta=\frac{10}{\sqrt{125}}$.

Answer:

$\frac{10}{\sqrt{125}}$