Answer:
x = 13
y = 13√2
Explanation:
Special right triangles are right triangles with specific angle measurements whose side lengths follow a certain pattern.
45-45-90 Triangle
A 45-45-90 special right triangle is a triangle that has two 45-degree angles and one 90-degree angle. Remember that in a right triangle, the two shorter sides are called the legs. Additionally, the longest side that is directly across from the right angle is the hypotenuse. In a special right triangle, the legs are equal. Additionally, the hypotenuse is √2 times the leg length. So, if x is the leg, then the hypotenuse is x * √2.
Solving For x and y
In the problem above, x represents one of the legs and y is the hypotenuse. Since this is a 45-45-90 triangle we know that the legs are equal, and one of the legs is 13 units. So, x must equal 13 as well. Then, we know that y must equal x * √2. So, y equals 13√2. This radical cannot be simplified any further, so the final answers are: