Question

find sin(c). round to the nearest hundredth if necessary.

Explanation:

Step1: Recall sine - ratio formula

The sine of an angle in a right - triangle is defined as $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. For angle $C$ in right - triangle $ABC$, the side opposite to angle $C$ is $AB$ and the hypotenuse is $AC$.

Step2: Identify the lengths

We are given that $AB = 5$ and $AC=13$.

Step3: Calculate $\sin(C)$

Using the formula $\sin(C)=\frac{AB}{AC}$, we substitute the values: $\sin(C)=\frac{5}{13}\approx0.38$.

Answer:

b. 0.38