# Given a right triangle #triangle ABC# with #C=90^circ#, if b=10, c=26, how do you find a?

multiply L.H.S and R.H.S. by 10

Check: using Pythagoras

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Complete the ratio

to get

There are right-angled triangles whose sides are rational numbers.

The sides are known as "Pythagorean Triples".

If you recognise that two given sides are in one of the triples, you can simply write down the length of the third side by simple multiplying.

Some of the common triples are:

There are infinitely many triples which can be created.

The third side will therefore be 12 to complete the triple

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To find side (a) of the right triangle (ABC), we can use the Pythagorean theorem, which states that in a right 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.

The Pythagorean theorem can be written as:

[ a^2 + b^2 = c^2 ]

Given that (b = 10) and (c = 26), we can plug these values into the equation and solve for (a):

[ a^2 + 10^2 = 26^2 ]

[ a^2 + 100 = 676 ]

Subtracting 100 from both sides:

[ a^2 = 576 ]

Taking the square root of both sides:

[ a = \sqrt{576} ]

[ a = 24 ]

So, (a = 24).

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