Question

1. john is building a fence and needs to find the length of the missing side. he needs to round his answer to the nearest tenth. what is the length of the missing side? 31.3 31.1 31.4 31.2

Explanation:

Step1: Identify trigonometric ratio

In a right triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 31^\circ$, opposite side is 16, hypotenuse is $x$. So $\sin(31^\circ)=\frac{16}{x}$.

Step2: Solve for x

Rearrange the formula: $x=\frac{16}{\sin(31^\circ)}$. Calculate $\sin(31^\circ)\approx0.5150$. Then $x=\frac{16}{0.5150}\approx31.1$.

Answer:

31.1