Given the triangle below, determine the missing side(s) without using the Pythagorean theorem (make sure your answer is fully simplified).

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Given the triangle below, determine the missing side(s) without using the Pythagorean theorem (make sure your answer is fully simplified).

Let's give this problem a try. So here it says, given the triangle below, determine the missing sides without using the pythagorean theorem, and make sure your answer is fully simplified. So as we can see, we have this right triangle, and we are missing the side x. And x would be the hypotenuse of this right triangle. Now I'm not allowed to use the Pythagorean theorem to find this missing value, but there are some things I notice about this right triangle. First off, I notice that we have 2 legs which are the same side on the triangle. I also notice we have a 45 degree angle. Whenever you see a 45 degree angle in a right triangle, the other angle has to be 45 degrees as well, because all the angles on the triangle have to add to a 180 degrees. And if this is 90, then these 2 have to be 45 to add to 180. So since we have this, we know that we have the special case of a 45, 45, 90 right triangle. So we can use the relationships that we've learned for these special cases. For a 45, 45, 90 triangle, the hypotenuse is equal to 1 of the legs multiplied by the square root of 2. So if I want to find this missing side, which is the hypotenuse, I can say here that x, our hypotenuse, is equal to one of the legs on the triangle, which we can see these are 9 multiplied by the square root of 2. And there's really nothing more I can do here to simplify what we just calculated. So 9 times the square root of 2 is the answer to this problem. So the missing side of this leg is or the missing side of this triangle is 9 times the square root of 2, and that is the answer. So hope you found this video helpful. Thanks for watching.