Answer:
Central Angle between two radii=120°
Radii of the circle = 24 m
When two sides of triangle are equal ,then angle opposite to them are equal.
120 + 2* (Measure of the angle )=180°
Measure of the two angles of the triangle [tex]=\frac{60 degree}{2}\\\\=30 degree[/tex]
[tex]Sin 30=\frac{P}{24}\\\\B=12 \\\\ Cos 30=\frac{B}{24}\\\\B=12 \sqrt{3}[/tex]
Base = 2*12√3=24√3 meter
Altitude of Triangle = 12 meter
Area of Shaded Region
= Area of Sector - Area of Triangle
[tex]=\frac{\pi *24*24*120}{360}- \frac{1}{2}*24\sqrt{3}*12\\\\=192*\pi - 144*\sqrt{3}[/tex]
Option B: (192 pi-144 √3 ) m²
