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 either 14,7,14√2, or 7√2
In a right triangle, if one angle is 45 degrees, then the other two angles are also 45 degrees each, since the sum of angles in a triangle is 180 degrees.
In the first triangle, the side opposite the 45 degree angle has a length of 10. Since we know that the opposite side and the hypotenuse are in a ratio of 1:√2 in a 45-45-90 triangle, the length of the hypotenuse is 10√2.
In the second triangle, the side opposite the 45 degree angle has a length of 14. Using the same logic as before, we can determine the length of the hypotenuse by multiplying the length of the opposite side by √2. Therefore, the length of the hypotenuse in the second triangle is 14√2.
So, the correct answer is 14√2.