Given: PFST is a rectangle m∠SOT = 60°, OS = R=4 Find: ST and PT

Accepted Solution

the complete question in the attached figure

we know that

radius r of a circle=4 units

in the triangle OST
OT=OS=4 units
m∠OST = 60°
cos 60°=(ST/2)/r-------> ST=2*r*cos 60°-----> 2*4*(1/2)----> 4 units
triangle OST 
it's an equilateral triangle

the answer Part a) is 
ST=4 units

Part b)
Find PT
in the triangle POT
m∠POT = (180°-60°)---------> 120°
m∠OTP = 30°
cos 30°=(PT/2)/r------> PT=2*r*cos 30°------> 2*4*√3/2----> 4√3 units

the answer Part b) is
PT=4√3 units