Pythagorean Theorem, with sides 3, 4 and 5, a sq x b sq = c sq
Quote from the Stanford Encyclopedia of Philosophy
Stanford Encyclopedia of Philosophy Pythagoras
Proclus does not ascribe a proof of the theorem to Pythagoras but rather goes on to contrast Pythagoras as one of those “knowing the truth of the theorem” with Euclid who not only gave the proof found in Elements I.47 but also a more general proof in VI. 31.
Speaking of Angry Old Men, it amazing how this article at This is Carpentry brought out the Angry Old Men on Common Rafter Framing.
Common Rafter Framing by Mike Sloggatt @ This is Carpentry
Using trigonometric ratios to calculate the lengths of the right triangles begins with the unit circle.
Trigonometric functions of the angle θ can be constructed geometrically in terms of a unit circle. In this next drawing the unit circle has an radius equal to 1 and the angle θ equals the roof slope angle of an 8:12 pitched roof.
In this next drawing the unit circle has an radius equal to 1 and the angle θ equals the hip rafter slope angle of an 8:12 pitched roof.