Question

q. solve for the missing distance.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine function is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 39^{\circ}$, the hypotenuse is $30$ m, and the opposite side is $d$.

Step2: Substitute the values into the sine formula

We have $\sin(39^{\circ})=\frac{d}{30}$.

Step3: Solve for $d$

Multiply both sides of the equation by $30$: $d = 30\times\sin(39^{\circ})$.
Using a calculator, $\sin(39^{\circ})\approx0.6293$.
So, $d=30\times0.6293 = 18.879\approx18.9$ m.

Answer:

$18.9$ m