Question

find the sine of ∠d.

right triangle efd with right angle at f, ef = 4, fd = 7, hypotenuse ed = √65

write your answer in simplified, rationalized form. do not round.

sin(d) = blank box fraction and square root buttons

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle D$, the opposite side is $EF = 4$, and the hypotenuse is $ED=\sqrt{65}$.

Step2: Apply the sine formula

Substitute the values into the formula: $\sin(D)=\frac{EF}{ED}=\frac{4}{\sqrt{65}}$.

Step3: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{65}$: $\frac{4\times\sqrt{65}}{\sqrt{65}\times\sqrt{65}}=\frac{4\sqrt{65}}{65}$.

Answer:

$\frac{4\sqrt{65}}{65}$