Circular segment

Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm, and the angle α = 60°.

Help formula: S = 1/2 r². (Β-sinβ)

Correct answer:

S =  20.1872 cm²
l =  15.6328 cm

Step-by-step explanation:

$$\begin{gathered} v=2 \\ A=60 \\ c=\cos (A/2)=\cos (60/2)\doteq 0.866 \\ \cos A/2=(r-v)/r \\ r\cdot \cos A/2=r-v \\ r=v/(1-c)=2/(1-0.866)\doteq 14.9282 \\ B=A°\to \text{rad}=A°\cdot \frac{\pi }{180}=60°\cdot \frac{3.1415926}{180}=1.0472=\pi /3 \\ S=1/2\cdot r^2\cdot (B-\sin (B))=1/2\cdot 14.9282^2\cdot (1.0472-\sin 1.0472)=20.1872{\text{cm}}^2 \end{gathered}$$

$l=A/360\cdot 2\pi \cdot r=60/360\cdot 2\cdot 3.1416\cdot 14.9282=15.6328\text{cm}$

Try another example