Question 1169864
Not sure about Pythagorean theorem and all that, but we can solve by
resolving the forces into horizontal and vertical components.
The tension, T, in the string is directed inward along the string.
In the y direction, there is a downward gravitational force equal to mg.
Since there is no acceleration in the y-direction, this must be balanced
by the y component of the tension, which is equal to Tsin(27).
Solving for T we get T = mg/sin(27) = 0.7*9.8/sin(27) = 15.11 N
There is a centripetal acceleration in the x-direction, which is 
provided by the x-component of the tension, Tcos(27), but this is not required
to solve the problem.