A right triangle has a hypotenuse of length 10√2 and an angle of 45 degrees, with a side opposite this angle with a length of 10. A second right triangle also has an angle of 45 degrees, with a side opposite this angle with a length of 14. Determine the length of the hypotenuse in the second triangle.
the hypotenuse of the second triangle has length 7√2
the hypotenuse of the second triangle has length 14√2
the hypotenuse of the second triangle has length 7
the hypotenuse of the second triangle has length 14
The length of the hypotenuse in the second triangle can be found using the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In the second right triangle, the side opposite the angle of 45 degrees has a length of 14. Let the other side have a length of x.
Applying the Pythagorean Theorem, we have:
x^2 + 14^2 = (hypotenuse length)^2
x^2 + 196 = (hypotenuse length)^2
Since the angle is 45 degrees and the side opposite this angle has a length of 14, both the other two sides must have the same length. Therefore, x is also equal to 14.
Substituting x = 14 into the equation above, we have:
14^2 + 196 = (hypotenuse length)^2
196 + 196 = (hypotenuse length)^2
392 = (hypotenuse length)^2
Taking the square root of both sides, we get:
√392 = hypotenuse length
The length of the hypotenuse in the second triangle is 14√2.