Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Use the sine function

In a right - triangle, the sine of an angle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 29^{\circ}$, the opposite side to the angle $M$ is $ON = x$, and the hypotenuse is $OM=6.8$. So, $\sin(29^{\circ})=\frac{x}{6.8}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin(29^{\circ})=\frac{x}{6.8}$ by $6.8$. We get $x = 6.8\times\sin(29^{\circ})$.
Since $\sin(29^{\circ})\approx0.485$, then $x = 6.8\times0.485=3.3$.

Answer:

$3.3$