Question

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

Explanation:

Step1: Recall sine definition

For an acute angle in a right triangle, $\sin(\theta)=\frac{\text{opposite side}}{\text{hypotenuse}}$.

Step2: Identify sides for $\angle X$

Opposite side to $\angle X$ is $VW=56$. First calculate hypotenuse $XW$ using Pythagorean theorem:
$$XW=\sqrt{XV^2 + VW^2}=\sqrt{33^2 + 56^2}=\sqrt{1089+3136}=\sqrt{4225}=65$$

Step3: Compute $\sin(X)$

Substitute values into sine formula:
$$\sin(X)=\frac{56}{65}$$

Answer:

$\frac{56}{65}$