a right triangle has a hypotenuse of length 16 and an angle of 45 degrees, with a side opposite this angle of length 8√2. a second right triangle also has an angle of 45 degrees and a side oppostie this angle with a length of 4√2. determind the length of the hypotenuse in the second triangle. the answer is not 8√2
Let's call the length of the hypotenuse in the second triangle "x". Now, let's use the sine function to find the length of the side opposite the 45-degree angle in the second triangle.
In the first triangle, the side opposite the 45-degree angle has a length of 8√2, and the length of the hypotenuse is 16. Using the sine function:
sin(45°) = (8√2) / 16
Simplifying:
1/√2 = (√2) / 2
√2 = 1
Now we can set up a ratio for the second triangle:
sin(45°) = (4√2) / x
1/√2 = (4√2) / x
Cross-multiplying:
x = 4√2 * √2
x = 4 * 2
x = 8
Therefore, the length of the hypotenuse in the second triangle is 8.