A 45-45-90 triangle has a hypotenuse of length 9. What is the length of one of its legs? If necessary, round your answer to two decimal places.

Question

mathmale · Answer

Because the two acute angles are = , the two shorter sides of the triangle (which we call the legs) are also = .  We could represent the length of one of these sides by x and the square of that by x^2.  What is the square of the length of the other leg?

Write an expression for the sum of the squares of the legs and equate that sum to the length of the hypotenuse (7) squared.

For review, the Pyth. Thm. says:$$a^2 + b^2=c^2,$$where a and b are the lengths of the shorter two sides and c is the length of the hypotenuse.  This assumes that the triangle is a RIGHT triangle.

anonymous · Answer

$$9^{2}=2a ^{2}$$

anonymous · Answer

$$a=9\sqrt{2}$$

anonymous · Answer

use calculator
helped
9/$$\sqrt{2}$$