1. Given: a = 10; b= 7Problem: find c.2. Given: C = 50; b = 40Problem: find a3. Proof of a 3,4,5 triangle.A right triangle can be constructed by making thesides 3, 4, and 5. We can prove it by the Law ofPythagoras.Since values of 3,4, and 5 satisfy the equation, wemay conclude that the statement above is correct.4. Application of the Law of PythagorasGiven a right triangle ABC:Prove that the area of a circle of a diameter of side c isequal to the sum of the areas of circles whose diametersare sides a and b.area circle diameter c = area circle diameter a + areacircle diameter b.Then:Since this is the rule of the right triangle, the abovestatement is true.Example:In the Y branch shown, the areas of the two branchesmust equal the area of the main. By the above proof, ifthe two known diameters are considered to be legs of aright triangle, the hypotenuse will be the diameter of themain.AII-23