Question

Can some body help me my mom won’t let me sleep until I find it

Answer 1

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

$\sqrt{3}/2 = DT /4$

DT =$2\sqrt{3}$ =  3.46

PT = 2*DT = 6.93