## Trigonometry (11th Edition) Clone

In a $45^{\circ}$ to $45^{\circ}$ right triangle the hypotenuse has a length that is $\sqrt 2$ time as long as either leg
1. Draw a square with sides equal to k 2. Draw diagonals and label them as c. The diagonal forms two isosceles right triangles. Each angle formed by a side of the square and the diagonal measures $45^{\circ}$ 3. Using the Pythagorean theorem express c (length of the diagonal) $k^{2}+k^{2}=c^{2}$ $2k^{2} = c^{2}$ $c= \sqrt {2k^{2}}$ $c= k\sqrt {2}$ Therefore, in a $45^{\circ}$ to $45^{\circ}$ right triangle the hypotenuse has a length that is $\sqrt 2$ time as long as either leg