Question

find the value of sin d rounded to the nearest hundredth, if necessary.

Explanation:

Step1: Recall the sine formula

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). For \(\angle D\), the side opposite to \(\angle D\) is \(EF\). First, find \(EF\) using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 13\) (hypotenuse) and \(a = 12\). Let \(b=EF\), then \(EF=\sqrt{13^{2}-12^{2}}=\sqrt{(13 + 12)(13 - 12)}=\sqrt{25}=5\).

Step2: Calculate \(\sin D\)

Now, using the sine formula \(\sin D=\frac{EF}{DF}\). Since \(EF = 5\) and \(DF=13\), then \(\sin D=\frac{5}{13}\approx0.38\).

Answer:

\(0.38\)