Question

1. the drawing shows the measurements in a section of a circular design. how long is the radius of the circle? f 10 cm g 8.7 cm h 7 cm j 4.3 cm

Explanation:

Step1: Identify the trigonometric relationship

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the opposite side to the \(30^{\circ}\) angle is \(5\) cm, and the hypotenuse is the radius \(x\) of the circle.

Step2: Apply the sine formula

We know that \(\sin30^{\circ}=\frac{5}{x}\). Since \(\sin30^{\circ}=\frac{1}{2}\), we have the equation \(\frac{1}{2}=\frac{5}{x}\).

Step3: Solve for \(x\)

Cross - multiply the equation \(\frac{1}{2}=\frac{5}{x}\) to get \(x = 5\times2\).

Answer:

F. \(10\) cm