Question

in circle m, diameters jl and hk each measure 16 centimeters. what is the approximate length of minor arc jh? round to the nearest tenth of a centimeter. 3.5 cm 6.9 cm 21.6 cm 46.8 cm

Explanation:

Step1: Find the radius of the circle

The diameter \(d = 16\) cm. The radius \(r=\frac{d}{2}\), so \(r = 8\) cm.

Step2: Find the central angle of arc \(JH\)

Since \(\angle KML=25^{\circ}\) and \(\angle JMH\) and \(\angle KML\) are vertical angles (opposite angles formed by two intersecting lines), \(\angle JMH = 25^{\circ}\).

Step3: Use the arc - length formula

The formula for the length of an arc \(s\) is \(s=\frac{n\pi r}{180}\), where \(n\) is the central angle and \(r\) is the radius.
Substitute \(n = 25\) and \(r = 8\) into the formula:

$$s=\frac{25\times\pi\times8}{180}=\frac{200\pi}{180}=\frac{10\pi}{9}\approx\frac{10\times 3.14}{9}=\frac{31.4}{9}\approx3.5$$

Answer:

3.5 cm