Question

what is the length of the side opposite ∠d? units sin(d) =

Explanation:

Step1: Identify opposite side

In right - triangle $\triangle DEF$ with right - angle at $E$, the side opposite $\angle D$ is $EF$. Given $EF = 5$ units.

Step2: Recall sine formula

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle D$, the opposite side is $EF = 5$ and the hypotenuse $DF=13$. So, $\sin(D)=\frac{EF}{DF}=\frac{5}{13}$.

Answer:

The length of the side opposite $\angle D$ is $5$ units.
$\sin(D)=\frac{5}{13}$