industrial application help

The two images below shows one of our attempts to come up with the rotation angle required. I believe that it does not work because we are using first order trig which assumes symmetry . Please comment on this assumption and or why it does not work. See attachment

Working with area and perimeter of a triangle

In triangle ABC, the lengths of line AB and line BC equal 13 centimeters. If the perimeter of triangle ABC is 36 centimeters, what is the area in square centimeters of triangle ABC?

Proofs!

I am trying to figure out how to prove opposite angles of a quadrilateral are supplementary.The quadrilateral is inscribed in the circle

Rigid Pentagonal Prism

How many lines would you need to add to a pentagonal prism anchored to the ground to make it rigid?

How to factor polynomials

Factor the polynomial: x2+4x-4=0