Question

Lenth of Arc whose central angle is X is 26.4 cm and radius of ciccle is 24 cm find the x

Answer 1

Answer:

42°

Step-by-step explanation:

perimeter of sector = x°/360 × 2πr

$\frac{x}{360} \times 2 \times \frac{22}{7} \times 24 = 26.4 \\ = \frac{x \times 2 \times 22 \times 24}{360 \times 7} = 26.4 \\ x = \frac{26.4 \times 360 \times 7}{2 \times 22 \times 24} \\ = \frac{26.4 \times 180 \times 7}{22 \times 24} \\ = \frac{26.4 \times 90 \times 70}{11 \times 24} \\ = \frac{26.4 \times 45 \times 7}{11 \times 12} \\ = \frac{13.2 \times 45 \times 7}{11 \times 6} \\ = \frac{13.2 \times 15 \times 7}{11 \times 3} \\ = \frac{13.2 \times 5 \times 7}{11} \\ = \frac{66 \times 7}{11} \\ = 6 \times 7 \\ = {42}^{o}$