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Step-by-step explanation:

These problems are based on triangle ratios. You cannot use the Pythagorean theorem to solve them.

The first triangle is a 45 45 90 degree triangle (I'm talking about the angles), and so, the ratio is 1:1:, so I have to divide the hypotenuse by to get the legs. The hypotenuse is 15, so that divided by is 15. X is the same length as y because of the triangle ratio, so both x and y for the first triangle are 15.

The second triangle is a 30 60 90 degree triangle, so the ratio is x:x:2x. The short leg is 7, so 7 * 2 is the hypotenuse, which is 14. The long leg is 7 * , which is 21. So, x for the second triangle is 14, and y for the second triangle is 21.

Question 9: x = , Question 10: y = , Question 11: x = , Question 12: y = 21

Step-by-step explanation:

Question 9-10: Right triangles with 45°, 45°, 90° have a special rule, the legs of the triangle are equal, so x = y. Now you can form the statement , and because x = , so does y.

Question 11-12: Right triangles with 30°, 60°, 90° also have a special rule, the side corresponding to 30° is half the length of the hypotenuse and the side corresponding to 60° is times as great as the 60°. x is 2 times as big as , so its length is . Y is as great as , so its length is 21.

step-by-step explanation:

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