Question

what is the approximate value of x? round to the nearest tenth. 6 cm 3.1 cm 3.9 cm 4.6 cm 5.4 cm

Explanation:

Step1: Identify trigonometric relation

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In this right - triangle, $\theta = 50^{\circ}$, the hypotenuse is $6$ cm and $x$ is the side opposite to the $50^{\circ}$ angle. So $\sin50^{\circ}=\frac{x}{6}$.

Step2: Solve for $x$

We can rewrite the equation as $x = 6\times\sin50^{\circ}$. Since $\sin50^{\circ}\approx0.766$, then $x=6\times0.766 = 4.596$.

Step3: Round the result

Rounding $4.596$ to the nearest tenth gives $4.6$.

Answer:

$4.6$ cm