Question

a pendulum swings through an angle of 30degree and describes an arc of length 8.8cm. find the length of the pendulum.

Answer 1

180º → πrad
30º → x

180x = 30πrad
$x = \frac{30 \pi rad}{180}\:simplify\:by\: \frac{\div30}{\div30} \to\:\boxed{x = \frac{\pi rad}{6}}$

Therefore:
$\frac{\pi rad}{6}} = \frac{Arc}{Pendulum}$
$\frac{\pi rad}{6}} = \frac{8.8}{Pendulum}$
multiply cross
$\pi rad*P = 6*8.8$
$\pi rad*P = 52.8$
$P = \frac{52.8}{\pi rad}$
If: 180º → πrad
We have:
$P = \frac{52.8}{180}$
$P = 0.29333...\:\to\:P\approx0.29\:or\:\boxed{\boxed{P\approx29cm}}\end{array}}\qquad\quad\checkmark$