Chapter 13: Triangles 177The side opposite the 60r angle must be half the hypotenuse times the square root of 3. So if you
know the side of an equilateral triangle in 8 inches long, the altitude will divide the base into two
segments, each 4 inches long, and the altitude itself will be 43 inches long, or approximately
6.9 inches.
The other special right triangle, another one that shows up a lot, is the 45-45-90 triangle, or the
isosceles right triangle. In an isosceles right triangle, the two legs are of equal length. You could
pick your favorite number for an example, but let’s say the legs are each 6 inches long. Apply the
Pythagorean theorem. The equation a^2 + b^2 = c^2 becomes 6^2 + 6^2 = c^2 , or c^2 = 72. Take the square
root and c, the length of the hypotenuse, is c 72 6 2. The hypotenuse of an isosceles right
triangle is equal to the length of the leg times the square root of 2.
Suppose the diagonal of a square is 9 cm. The diagonal of the square is the hypotenuse of an
isosceles right triangle, so if that is equal to 9, and you know it’s supposed to be equal to the side
times the square root of 2, you can say s 29 and s
9
2
6.4.
SideSide45°45°Hypotenuse =
side times the square root of 29