Question

Find the length of AC

Answer 1

The rule of the length of an arc is

`L=(x)/(360)*2\pi\text{ r}`

Where L is the length of the arc

x is the central angle subtended by the arc

r is the radius of the circle

∵ BC = r

∵ BC = 16 ft

∴ r = 16

∵ < ABC is a central angle subtended by the arc AC

∴ ∵ < ABC = 51 degrees

∴ x = 51

→ Substitute the values of x and r in the rule above to find The length of arc AC

`\begin{gathered} AC=(51)/(360)*2*3.14*16 \\ AC=14.23466667 \end{gathered}`

→ Round it to 2 decimal places

∴ AC arc = 14.23 ft