OT = 4
PT = 6.93
Explanation :
OS = OT = R = 4
Hence ∠OTS = ∠OST, (Angles opposite to equal sides are equal)
∠TOS + ∠OTS + ∠OST = 180°
60° + ∠OTS + ∠OST = 180°
2∠OTS = 180° - 60° (∠OTS = ∠OST)
Hence, ∠TOS = ∠OTS = ∠OST = 60°
Hence, ΔOST is an equilateral triangle,
Therefore, OS = OT = ST = 4
Let us draw a perpendicular from OD on PT.
ΔODT is a right angled triangle
∠DTO = 90° - ∠OTS = 30° (Angle of a rectangle is 90°)
in ΔDTO,
cos 30° = DT/OT
[tex]\sqrt{3}/2 = DT /4[/tex]
DT =[tex]2\sqrt{3}[/tex] = 3.46
PT = 2*DT = 6.93
