Question

applying the sine ratio
what is the length of the side opposite ∠d?
units
sin(d) =
triangle def: ∠e is a right angle, de = 12, ef = 5, df = 13

Explanation:

Step1: Identify side opposite ∠D

In right triangle \(DEF\) (right-angled at \(E\)), the side opposite angle \(D\) is the side not connected to \(D\), which is \(EF\). From the diagram, \(EF = 5\) units.

Step2: Recall sine ratio definition

The sine of an angle in a right triangle is \(\sin(\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}\). For \(\angle D\), hypotenuse is \(DF = 13\) units, opposite side is \(5\) units.
<Expression>
$\sin(D)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{5}{13}$
</Expression>

Answer:

Length of side opposite ∠D: 5 units
$\sin(D) = \frac{5}{13}$