a right triangle has a hypotenuse of length 16 and an angle of 45 degrees, with a side opposite this angle of length \sqrt2. a second right triangle also has an angle of 45 degrees and a side oppostie this angle with a length of 4\sqrt2. determind the length of the hypotenuse in the second triangle
In a right triangle, the hypotenuse is always the longest side. So, in the second right triangle, the side opposite the 45-degree angle, which has a length of 4√2, cannot be the hypotenuse.
Let’s call the hypotenuse of the second triangle "x". According to the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can write the equation as follows:
(x²) = (4√2)² + (√2)²
Simplifying the equation:
x² = 32 + 2
x² = 34
Taking the square root of both sides:
x = √34
Therefore, the length of the hypotenuse in the second triangle is √34.