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Solving right Triangles means we need to find the measures of other two angles (as one angle is of 90^{0}) or the measures of sides of the Right Triangle. 
Pythagorean Theorem states that Square of the hypotenuse are equal to the sum of squares of the base and perpendicular.
AC=hypotenuse AB=perpendicular CB=base
(Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2}
If we know the measure of any two sides we can find the other side easily.
Hypotenuse = √ [(Base)^{2} + (Perpendicular)^{2}]
Base = √ [(Hypotenuse)^{2} − (Perpendicular)^{2}]
Perpendicular =√ [(Hypotenuse)^{2}−(Base)^{2}]
It is used to find the length of different sides of right angled triangle. It can be defined by geometric proof and algebraic proof. It is not only defined for Euclidean figures but also for n – dimensional shapes that are Solid in form.
As per Pythagorean Theorem Trigonometry:
Sin^{2} ø + cos^{2} ø = 1
By Trigonometry Pythagorean Theorem identity we get,
Sin ø = opposite side/hypotenuse,
Cos ø = adjacent/ hypotenuse,
The Pythagorean identity we get,
Opposite^{2}+ adjecent^{2} = 1
Hypotenuse^{2}
If we take an example in which value of base is equal to 12 units (B = 12) and the value of hypotenuse is equal to 13 units (C = 13) which is a right angled triangle then find the value of perpendicular (A = ?) .
Solution: According to the Pythagorean Theorem:
(13)^{2} = (12)^{2} + (perpendicular)^{2}
=> (A)^{2} = (C)^{2}  (B)^{2}
=> (A) ^{2} = (13)^{2}  (12)^{2}
=> (A) = √ [(13)^{2}  (12)^{2}]
=> (A) = √ [(169)  (144)]
=> (A) = √ 25
=> (A) = 5 unit.
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