Question

The area of a sector is 30 cm2 and its arc length is 8.5 cm. Find the angle of the sector, giving your answer correct to the nearest degree

Answer 1

area of sector = @/360× πr² = 30cm²

length of arc = @/360 × 2πr = 8.5cm

for finding radius r taking ratio of area and lenth of arc

area of sector = @/360 ×πr² = 30cm²

____________________________

length of arc = @/360× 2πr = 8.5cm

ratio =

r /2 = 30/8.5

r= 60/8.5 = 7.05cm

let find angle

area of sector = @/360× πr² = 30cm²

@ = 30 × 360 × 1 / π × 1 / 7.05²

@= 77.12°