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 oppoite this angle with a length of 14. determine the length of the hypotenuse in the second triangle
the answer is not 2√74
To find the length of the hypotenuse in the second triangle, we can use the Pythagorean theorem.
In the first triangle, we have a side length of 10 and an angle of 45 degrees. The hypotenuse can be found using the equation:
hypotenuse^2 = side^2 + side^2
hypotenuse^2 = 10^2 + 10^2
hypotenuse^2 = 100 + 100
hypotenuse^2 = 200
hypotenuse = √200
Since the given length of the hypotenuse is 10√2, we can conclude that √200 = 10√2.
In the second triangle, we have a side length of 14 and an angle of 45 degrees. To find the length of the hypotenuse, we can use the same equation:
hypotenuse^2 = side^2 + side^2
hypotenuse^2 = 14^2 + 14^2
hypotenuse^2 = 196 + 196
hypotenuse^2 = 392
hypotenuse = √392
However, √392 is not equal to 2√74. We made a mistake in our calculations.
Let's correct it:
√392 = √(16 * 49) = √(4 * 4 * 7 * 7) = 4 * 7 = 28
Therefore, the length of the hypotenuse in the second triangle is 28.