Elaboration of unknown side cases on Pythagoras Theorem (#22373)

-I decided to extend the amount of information on Pythagoras Theorem, through explaining other cases of finding an unknown side apart from the hypotenuse, which are the perpendicular height and base.
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KevinatorTrainer5
2018-11-22 01:52:03 +11:00
committed by Tom
parent 8ca6a28a9b
commit df0bb71bce

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@ -13,7 +13,31 @@ The theorem states:
c<sup>2</sup> = a<sup>2</sup> + b<sup>2</sup>
c = &radic;(a<sup>2</sup> + b <sup>2</sup>), where c > 0
Whenever you are given two sides of a right triangle, you can calculate the third one using the Pythagorean Theorem.
In some instances, the value of the perpendicular height or the base may not be given, but the value of the hypotenuse can be given. So in this case:
Let c become the length of the hypotenuse, a become the length of the perpendicular, and b become the length of the height. The Pythagoras Theorem is given by:
a<sup>2</sup> + b<sup>2</sup> = c<sup>2</sup>
The first case will be finding the unknown value of the perpendicular height, which is 'a'. So firstly, we will make a<sup>2</sup> become the subject:
a<sup>2</sup> = c<sup>2</sup> - b<sup>2</sup>
And then, we will square root both sides to get the value of a:
a = &radic;(c<sup>2</sup> - b<sup>2</sup>)
For the second case, we will be finding the unknown value of the base, which is 'b'. So we will firstly make b<sup>2</sup> become the subject:
b<sup>2</sup> = c<sup>2</sup> - a<sup>2</sup>
And then, we will square root both sides to get the value of b:
b = &radic;(c<sup>2</sup> - a<sup>2</sup>)
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