Question

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

Explanation:

Step1: Recall sine - ratio definition

$\sin(E)=\frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Identify sides

The side opposite $\angle E$ is $DF$. Using Pythagorean theorem, $DF = \sqrt{10^{2}-8^{2}}=\sqrt{100 - 64}=\sqrt{36}=6$. Hypotenuse is $EF = 10$.

Step3: Calculate sine value

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

Answer:

$\frac{3}{5}$