A right triangle has a hypotenuse of length 10sqrt(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. (point) The hypotenuse of the second triangle has length 7sqrt(2) The hypotenuse of the second triangle has length 14. The hypotenuse of the second triangle has length 14sqrt(2) The hypotenuse of the second triangle has length 7.
To determine the length of the hypotenuse in the second triangle, we can use the sine function.
In the first triangle, sin(45°) = opposite/hypotenuse = 10/10√2 = 1/√2 = √2/2.
In the second triangle, we are given the length of the opposite side as 14. Using the sine function, we have sin(45°) = opposite/hypotenuse = 14/hypotenuse.
Setting these two expressions equal to each other, we have √2/2 = 14/hypotenuse.
Cross multiplying gives us √2 * hypotenuse = 2 * 14, which simplifies to hypotenuse = 2sqrt(2) * 14/√2 = 28.
Therefore, the length of the hypotenuse in the second triangle is 28.
None of the provided options match this answer, so none of them are correct.