Question

Find the missing side lengths

Put answers as radicals in simplest form
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Answer 1

We have a right triangle with an angle of 45 degrees. The side lengths are x, y, and 2√2.

In a 45-45-90 triangle, the two legs are congruent, so we can set x = y.

Using the Pythagorean theorem, we can relate the side lengths of the triangle:

x^2 + x^2 = (2√2)^2

2x^2 = 8

x^2 = 4

x = √4

x = 2

Therefore, the missing side lengths are:

x = 2

y = 2

So, the side lengths of the triangle are 2, 2, and 2√2.

Explanation: