Question

1. determine the length of side s to the nearest tenth of a millimetre.

a. 7.3 mm
b. 15.7 mm
c. 8.1 mm
d. 37.1 mm

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, we know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 25^{\circ}$, the opposite side to the angle $\theta$ is the side with length $s$ and the hypotenuse is $17.3$ mm.
So, $\sin25^{\circ}=\frac{s}{17.3}$.

Step2: Solve for $s$

We can re - arrange the equation to get $s = 17.3\times\sin25^{\circ}$.
Since $\sin25^{\circ}\approx0.4226$, then $s=17.3\times0.4226 = 7.30098\approx7.3$ mm.

Answer:

a. 7.3 mm