If angles QNM, QNP, and MNP are right angles, find the length of NQ.
This is a flat pattern of the part from the original diagram.
Red dotted lines are bend lines.
NQ = NP = sin30º * 120 NQ = 60
Since QNP is a right angle and angle QPN = 45 then angle PQN = 45
Then y = h
And since QNM is a right angle then triangle QMN is a 30-60-90 right triangle
Then x = sqrt (3) h
And MNP is a right triangle with angle MNP =90...so....
Using the Pythagorean Theorem
120^2 = x^2 + y^2
120^2 = 3h^2 + h^2
120^2 = 4h^2 take the square root of each side
120 = 2h
h = 60 = QN