Question

PLEASE HELP! Find the indicated side of the triangle.

Answer 1

9514 1404 393

Answer:

  a = b = 28/√2

Step-by-step explanation:

The ratios of side lengths in an isosceles right triangle are ...

  1 : 1 : √2 = a : b : 28

If we multiply the first ratio numbers by 28/√2, we get ...

  1 : 1 : √2 = (28/√2) : (28/√2) : 28

That is, ...

  a = b = 28/√2

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Alternate solution

Once you realize the triangle is isosceles, so that a=b, then you can use the Pythagorean theorem.

  a^2 + a^2 = 28^2

  2a^2 = 28^2 . . . . . . simplify

  a√2 = 28 . . . . .  take the positive square root

  a = b = 28/√2

Answer 2

Answer:

Step-by-step explanation:

Because a and b are both opposite 45 degree angles, a=b. Using the Pythagorean Theorem we can say.

$2a^2=28^2\\ \\ 2a^2=784\\ \\ a^2=\frac{784}{2}\\ \\ a=\sqrt{\frac{784}{2}}\\ \\ a=\frac{28}{\sqrt{2}}$