Question

ac =
round your answer to the nearest hundredth.

Explanation:

Step1: Use trigonometric relation

In right - triangle $ABC$ with $\angle B = 35^{\circ}$ and hypotenuse $AB = 5$, and we want to find the side $AC$ which is opposite to $\angle B$. We use the sine function. The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\sin B=\sin35^{\circ}=\frac{AC}{AB}$.

Step2: Solve for $AC$

We know that $AB = 5$ and $\sin35^{\circ}\approx0.5736$. Substituting the values into the formula $\sin B=\frac{AC}{AB}$, we get $AC = AB\times\sin B$. So, $AC=5\times\sin35^{\circ}$.
$AC = 5\times0.5736 = 2.868\approx2.87$.

Answer:

$2.87$