find the value of x.\nx≈\n(simplify your answer. type a whole number. round to the nearest degree as needed.)

Explanation:

Step1: Identify trigonometric ratio

In a right - triangle, we use the sine ratio. $\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the opposite side to angle $x$ is $3.7$ and the hypotenuse is $5.1$. So, $\sin(x)=\frac{3.7}{5.1}$.

Step2: Solve for $x$

We know that $x = \sin^{- 1}(\frac{3.7}{5.1})$. Calculate $\frac{3.7}{5.1}\approx0.7255$. Then $x=\sin^{-1}(0.7255)$. Using a calculator, $x\approx46.5^{\circ}$.

Step3: Round to the nearest degree

Rounding $46.5^{\circ}$ to the nearest degree gives $47^{\circ}$.

Answer:

$47$