Hi again, i'm currently studying for my pure maths intermediate level exam and i need some help with a trigonometry question please:
The points A and B lie on the circumference of a circle center O and radius
r cm, such that the angle AOB = θ radians. The sector AOB has area 9cm^2 and the total perimeter of sector AOB is 15cm.
a)Show that r satisfies the equation 2r^2 - 15r + 18 = o
b)Find the value of θ,explaining why there is only one possible value.
I know that area of sector = (1/2).(r^2).(θ)
not sure if perimiter of sector would be length of arc + radius x2
Any help is appreciated,thanks!
*sry i meant sector not segment in thread title
the two equations are
1)15 = r(θ+2)
2)9 = 1/2r^2θ
from 1) i get θ = 15/r -2 and i substitute it in 2)
which gives 9= 1/2r^2(15/r - 2)
9= 1/2(15r - 2r^2)
18= 15r - 2r^2
2r^2 - 15r + 18 = o
part b) by factorising u get r = 6 r = 3/2
using 1) 15= 6(θ+2) 2) 15= 3/2(θ+2)
θ = 1/2 θ = 8
The last thing I want to ask regarding question b) is why is there only one possible value of θ?