Question

Can somebody help me out my mom won’t let me sleep until I do it

Answer 1

Check the picture below.

$\bf \textit{arc's length for }\mathbb{ST}\\\\ s = \cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r= 4\\ \theta =60 \end{cases}\implies s = \cfrac{\pi (60)(4)}{180}\implies s = \cfrac{4\pi }{3}\implies s\approx 4.2 \\\\[-0.35em] ~\dotfill$

$\bf \textit{arc's length for }\mathbb{PT}\\\\ s = \cfrac{\pi \theta r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\[-0.5em] \hrulefill\\ r= 4\\ \theta =120 \end{cases}\implies s = \cfrac{\pi (120)(4)}{180}\implies s = \cfrac{8\pi }{3}\implies s \approx 8.4$