~F.2 Maths X1

pyth. theorem 做法:
PS. 我以(2)代替2次方,因為打唔到

∵ OAB is an equilateral triangle
∴AB=OB=10cm
draw a line OF which is perpendicular to AB
FB=AB/2=5cm
OF (2)+FB(2)=OB(2) (pyth. theorem)
OF(2)+5(2)=10(2)
OF(2)+25=100
OF(2)=75
OF=8.660(corr. to 4 sig. fig.)
∴The radius of the sector OCD is 8.660 cm

trigonometry 做法:
∵ OAB is an equilateral triangle
∴∠OBA=60∘(property of eq. tri.)
draw a line OF which is perpendicular to AB
sin60∘=OF/OB
sin60∘=OF/10
OF=10sin60∘
∴OF=8.660(corr. to 4 sig. fig.)
∴The radius of the sector OCD is 8.660 cm

Firstly, draw a line from O to the mid-point of AB
and name the point X, OX is the radius of the sector OCD
Then, AX = XB = 5 cm
By pythagorus therom,
OA2 = OX2 + AX2
10x10 = OX2 + 5x5
100=OX2 +25
OX2 = 75
OX = 8.66 cm