Question

what is the approximate value of x? round to the nearest tenth.
triangle with right angle, one angle 50°, hypotenuse 6 cm, side x opposite 50°, side y adjacent to 50°; options: 3.1 cm, 3.9 cm, 4.6 cm, 5.4 cm

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle with an angle of \(50^{\circ}\), the hypotenuse is \(6\) cm, and \(x\) is the side opposite to the \(50^{\circ}\) angle. The sine function is defined as \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(50^{\circ})=\frac{x}{6}\).

Step2: Solve for \(x\)

To find \(x\), we can re - arrange the formula: \(x = 6\times\sin(50^{\circ})\). We know that \(\sin(50^{\circ})\approx0.7660\). Then \(x=6\times0.7660 = 4.596\approx4.6\) (rounded to the nearest tenth).

Answer:

\(4.6\) cm