0
$\begingroup$

A right angled triangle has side lengths labeled as so.

A common geometric construction that shows three squares sitting upon the sides of a right triangle with lengths A, B, and C

However unlike in this diagram $a = b$.

How can $a$ be calculated given $c$?

Would $a = c \cdot d$ where $d$ is a constant?

  • 0
    A suggestion: the use of $N$ as a variable is prone to make people think it is a natural number, so it should be avoided. $D$ would be a better choice.2011-03-15

2 Answers 2

6

We know that $c^2 = a^2+b^2$ from Pythagorean Theorem or $c^2 = 2a^2$. Thus $c = a \sqrt{2}$.

  • 2
    ... and so $a = \frac{c}{\sqrt{2}}$, making $N = \frac{1}{\sqrt{2}} \approx 0.7071$2011-03-15
2

If A=B , then the angles of the triangle are 45:45:90, And as per the 45:45:90 theorem, the side opposite the 45 degree angle is hypotenuse/√2

So in this case value of A will be C/√2