PYTHAGOREAN THEOREM
In a right triangle, the square of the length of the hypotenuse equals the sum
of the squares of the lengths of the legs.
Thus, in Fig. 1.1, c2 = a2 + b2
Fig. 1.1
Tests for Right, Acute, and Obtuse Triangles
If c2 = a2 + b2 applies to the three sides of a triangle, then the triangle is a right triangle; but if c2 ≠ a2 + b2, then the triangle
is not a right triangle.
In ABC, if c2 < a2 + b2 where c is the longest side of the triangle, then the triangle is an acute triangle.
Thus in Fig. 1.2, 92 < 62 + 82 (that is, 81 < 100); hence, ABC is an acute triangle.
In ABC, if c2 > a2 + b2 where c is the longest side of the triangle, then the triangle is an obtuse triangle.
Thus in Fig. 1.3, 112 > 62 + 82 (that is, 121 > 100); hence, ABC is an obtuse triangle.
Fig. 1.2
Fig. 1.3
Finding the sides of a right triangle

If leg a is the missing side, then transform the equation to the form: a = √(𝑐 2 − 𝑏 2 )

If leg b is unknown, then: b = √(𝑐 2 − 𝑎2 )

For hypotenuse c missing, then: c = √(𝑎2 + 𝑏 2 )