45°
b
a
35
Help me if you can

9514 1404 393

Answer:

  C)  a = 3√10; b = 3√5

Step-by-step explanation:

The side ratios in an isosceles right triangle are 1 : 1 : √2. This is a fact worth remembering. You know the triangle is isosceles because both acute angles are 45°, which means both legs are the same length.

If the leg lengths are 1, the Pythagorean theorem tells you the hypotenuse is ...

  c^2 = a^2 + b^2 . . . . . . for legs a, b, and hypotenuse c

  c^2 = 1^2 + 1^2 = 2

  c = √2

This tells you the leg : leg : hypotenuse ratios are as shown above.

__

What that means here is that b = 3√5, the same length as the one shown. It also means that ,,,

  a = (3√5)(√2) = 3√(5·2)

  a = 3√10

The only answer choice with the correct value of 'a' is (C).

  a = 3√10, b = 3√5

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