Find the lengths of the missing sides in the triangle. Round to the nearest tenth. The diagram is not to scale y x 45 13 right triangle
To find the missing sides in the right triangle, we can use the Pythagorean theorem, which states that for any right triangle, the sum of the squares of the two legs (the shorter sides) is equal to the square of the hypotenuse (the longest side).
In this case, we are given that one of the legs has a length of 13 units. Let's call the other leg y and the hypotenuse x.
Using the Pythagorean theorem, we have the equation:
13² + y² = x²
We are also given that one of the angles is 45 degrees. This means that the two legs are congruent, so y = 13 units.
Now we can substitute this value into the equation:
13² + 13² = x²
169 + 169 = x²
338 = x²
To find the value of x, we take the square root of both sides:
√338 ≈ 18.4
Therefore, the length of the hypotenuse (x) is approximately 18.4 units.