Question

How would I solve this?

Answer 1

You had the right idea using the Pythagorean theorem to solve for b.

Problem is for that triangle to work, the 5 and the 2√2 would have to switch places. The length of a leg cannot be larger than the length of the hypotenuse for it to truly be a right triangle.

Pythagorean theorem only works for the right triangles. Only way to "solve this problem would be to bring in complex numbers.

5² + b² = (2√2)²

25 + b² = 2²(√2)²

25 + b² = 4(2)

25 + b² = 8

b² = 8 - 25

b² = - 17

b = √-17

b= (√17i)

Then the problem with THIS is a measurement/distance cannot be negative... which goes against exactly what that complex number i is.