Question

use the following triangle to find sin(θ). rationalize any denominators containing radicals that you encounter in the answer. enter the exact fully simplified answer

Explanation:

Step1: Recall sine - definition

The sine of an angle $\theta$ in a right - triangle is defined as $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify opposite and hypotenuse

The side opposite to the angle $\theta$ has length $9$, and the hypotenuse has length $\sqrt{134}$.

Step3: Calculate $\sin(\theta)$

$\sin(\theta)=\frac{9}{\sqrt{134}}$.

Step4: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{134}$: $\sin(\theta)=\frac{9\sqrt{134}}{134}$.

Answer:

$\frac{9\sqrt{134}}{134}$