Question

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

Explanation:

Step1: Identify the triangle type and trigonometric ratio

This is a right - triangle. We know the hypotenuse \(c = 6\) cm and we want to find the length of the side \(x\) which is 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 \(x\)

We can re - arrange the formula to solve for \(x\): \(x = 6\times\sin(50^{\circ})\). 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