Pythagorean Theorem Is our Understanding That The Hypotenuse (The Side Opposite The right Angle) Is always The Largest. This Can Be Used To Find All Three Sides As well as Figuring Out if A Triangle is right angled

Reverse Pythagoras Is When We are given two sides and are asked to find out if the triangle is right angled in which the hypotenuse is the largest

If A = 7m, B = 9m and C^2 = A^2 + B^2 then C^2 = 49 + 81 so C^2 = 130m but We need C so we square root 130 To Get C = 11.4m which is the largest side

If X^2 = C^2 - A^2 and C = 13, A = 6 Then X^2 =169 - 36 so X^2 = 133 and X is 11.5m Which is Shorter than The Hypotenuse

In Trigonometry we use Sine and Cosine to find out the Angle or side of any triangle by matching pairs and trios to find Angles, Sides and Areas

If we have side a = 10m, side b = 7m and angle C is = 25 Degrees then 1/2 x 10 x 7 x Sin(25) = 1/2 x 70 x Sin(25) we get 35 x Sin(25) therefore Area = 14.8m^2

If Side a is 15cm, Angle A is 35 degrees and Angle B is 42 degrees we use a / Sin(A) = b / Sin(B) we get (15 / SIn(35)) x Sin(42) we get b = 17.5cm

If Angle A = 46 degrees, Side a = 34cm and side b = 23cm we use Sin(A) / a = Sin(B) / b to get Sin(46) / 34 = Sin(B) / 23 therefore Sin(B) = (Sin(46) / 34) x 23 so Sin(B) = 0.486612 then Sin^-1(0.486612) and B = 29 Degrees

Prism V = B × h B = Area of base, (B = side2 or length.breadth) h = Height

Cylinder V = πr2h r = Radius of the circular base h = Height