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Answer:
Pythagorean theorem is mainly used for finding the length of the third side of a right angled triangle if the lengths of other two sides are known.
For this, it is more useful if the theorem is stated in terms of the length of the sides of the triangle.
Consider a right angled triangle with sides of lengths p,b and h, where p,b and h are the lengths of perpendicular,base and hypotenuse respectively.
Draw squares on each of these sides.These squares have areas p²,b² and h².
For any right angled triangle with sides of length p,b and h;
[tex] \: \: \: \: \: \: \: {h}^{2} = {p}^{2} + {b}^{2} ....................(i)[/tex]
[tex] \therefore \: h = \sqrt{ {p}^{2} + {b}^{2} } [/tex]
From (i); p²=h²-b²
[tex] \therefore \: p = \sqrt{ {h}^{2} - {b}^{2} } [/tex]
Similarly,
[tex]b = \sqrt{ {h}^{2} - {p}^{2} } [/tex]
Step-by-step explanation:
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