Question

find the sine of ∠d. simplify your answer and write it as a proper fraction, improper fraction, or whole number. sin(d) =

Explanation:

Step1: Recall sine definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify sides for ∠D

For ∠D, opposite side is $EF$, hypotenuse is $DE = 53$. First, find $EF$ using Pythagoras: $EF = \sqrt{DE^2 - DF^2} = \sqrt{53^2 - 28^2} = \sqrt{2809 - 784} = \sqrt{2025} = 45$.

Step3: Calculate sin(D)

$\sin(D) = \frac{EF}{DE} = \frac{45}{53}$.

Answer:

$\frac{45}{53}$