Question

what is the approximate value of x? round to the nearest tenth.
what is the approximate value of x? round to the nearest tenth.
6 cm
50°
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 the right - triangle, the angle $\theta = 50^{\circ}$, the hypotenuse is $6$ cm and the side opposite to the $50^{\circ}$ angle is $x$.
So, $\sin(50^{\circ})=\frac{x}{6}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin(50^{\circ})=\frac{x}{6}$ by $6$: $x = 6\times\sin(50^{\circ})$.
We know that $\sin(50^{\circ})\approx0.766$. Then $x=6\times0.766 = 4.596$.

Step3: Round to the nearest tenth

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

Answer:

$4.6$ cm