Question

find the value of x. round to the nearest tenth
37°
12
x
o 9.6
o 9
o 19.9
o 7.2

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 37^{\circ}$, the hypotenuse is 12 and the opposite side to the angle $37^{\circ}$ is $x$. So, $\sin37^{\circ}=\frac{x}{12}$.

Step2: Solve for $x$

We know that $\sin37^{\circ}\approx0.6018$. Then $x = 12\times\sin37^{\circ}$. Substituting the value of $\sin37^{\circ}$, we get $x=12\times0.6018 = 7.2216$.

Step3: Round the result

Rounding $7.2216$ to the nearest tenth gives $7.2$.

Answer:

D. 7.2