Answer:
1) m = 9/2, n = 9
3) x = y = (3√2)/2
Explanation:
1) We have a 30°-60°-90° right triangle, so the length of the longer leg is √3 times the length of the shorter leg, and the length of the hypotenuse is twice the length of the shorter leg. The length of the longer leg is (9√3)/2, so m, the length of the shorter leg, is 9/2, and n, the length of the hypotenuse, is 18/2, or 9.
3) We have an isosceles right triangle, so the length of the hypotenuse is √2 times the length of each leg. The length of the hypotenuse is 3, so x and y, the lengths of the two congruent legs, are 3/√2, or (3√2)/2.