Question

An isosceles right triangle has a hypotenuse of 6. what is the length of each leg? leave your answer as a simplified root or approximate your answer to the nearest tenths.

Answer 1

Explanation:

The altitude in this case would be against the hypotenuse.

SO, for this, the legs for this side are 6 and 6. This makes it a 45 - 45 - 90 triangle, which brings up something cool: we already know the length of the hypotenuse. 45 - 45 - 90 = x - x - x*squareroot(2) Therefore, the length of the hypotenuse is 6squareroot(2)

This brings another funny fact: the altitude, because it is an isoceles right triangle, perfectly splits the hypotenuse in half. In this case, the "squareroot(2)" acts as a variable (6/2=3) and does not affect the 6 or 3.

This brings up yet another sweet thing: It just made another isoceles right triangle, except instead of the legs being 6 and 6, the legs are 3squareroot(2). The altitude is one of the legs now, and thus the altitude's length is 3squareroot(2).