Question

find the sine of ∠e.
triangle image with right angle at d, fd=6, ed=√11, fe=√47
write your answer in simplified, rationalized form. do not round.
sin(e) = blank with fraction and square root buttons

Explanation:

Step1: Recall SOHCAHTOA for sine

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle E$, the opposite side to $\angle E$ is $FD = 6$, and the hypotenuse is $FE=\sqrt{47}$.

Step2: Apply the sine formula

So, $\sin(E) = \frac{\text{opposite to } \angle E}{\text{hypotenuse}} = \frac{6}{\sqrt{47}}$.

Step3: Rationalize the denominator

Multiply numerator and denominator by $\sqrt{47}$: $\frac{6\times\sqrt{47}}{\sqrt{47}\times\sqrt{47}} = \frac{6\sqrt{47}}{47}$.

Answer:

$\frac{6\sqrt{47}}{47}$