Question

given right triangle def, what is the value of sin(e)?

Explanation:

Step1: Recall sine - ratio definition

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

Step2: Identify side lengths

We are given that $EF = 10$ and, using the Pythagorean theorem $DF=\sqrt{EF^{2}-DE^{2}}=\sqrt{10^{2}-8^{2}}=\sqrt{100 - 64}=\sqrt{36}=6$.

Step3: Calculate $\sin(E)$

$\sin(E)=\frac{DF}{EF}=\frac{6}{10}=\frac{3}{5}$.

Answer:

$\frac{3}{5}$