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Sure! Let’s solve the Pythagorean theorem with an example.
The Pythagorean theorem states that in a rightangled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let’s consider a rightangled triangle with two known side lengths, a = 3 units and b = 4 units. We need to find the length of the hypotenuse, c.
Using the Pythagorean theorem, we can write the equation as:
c^2 = a^2 + b^2
Substituting the given values, we have:
c^2 = 3^2 + 4^2
c^2 = 9 + 16
c^2 = 25To find c, we take the square root of both sides:
c = √25
c = 5Therefore, the length of the hypotenuse (c) in this triangle is 5 units.
So, in this example, a rightangled triangle with side lengths of 3 units and 4 units has a hypotenuse of 5 units, as determined by the Pythagorean theorem.