Question

find the value of sin d rounded to the nearest hundredth, if necessary.

triangle def with right angle at e, fe = 5, fd = 7

Explanation:

Step1: Recall Sine Definition

In a right triangle, $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$. For $\angle D$, the opposite side to $\angle D$ is $EF = 5$, and the hypotenuse is $DF = 7$.

Step2: Calculate $\sin D$

Using the sine formula, $\sin D = \frac{EF}{DF} = \frac{5}{7}$.

Step3: Compute and Round

Calculate $\frac{5}{7} \approx 0.7142857$, then round to the nearest hundredth: $0.71$.

Answer:

$0.71$