Solve for x. Round your answer to the nearest tenth. In order to receive full credit, please show all work.
the sides are hypotenuse 21, 19, x
To solve for x, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b):
c² = a² + b²
In this case, the hypotenuse (c) is 21 and the other side (a) is 19:
21² = 19² + x²
Simplifying this equation gives:
441 = 361 + x²
Subtracting 361 from both sides:
441 - 361 = x²
80 = x²
To solve for x, we take the square root of both sides:
√(80) = √(x²)
Since x represents the length of a side in a right triangle, x cannot be negative, so the positive square root of 80 is taken:
√(80) ≈ 8.94
Therefore, the length of the third side (x) is approximately 8.94.