Question

find the length of side x in simplest radical form with a rational denominator.
triangle image: right triangle with two 45° angles, one leg labeled 1, the other leg labeled x
answer attempt 2 out of 2

Explanation:

Step1: Identify triangle type

This is a right isosceles triangle (two 45° angles), so the legs are equal, and we can use trigonometry. The side of length 1 is the hypotenuse, and $x$ is a leg.

Step2: Use cosine definition

Cosine of 45° equals adjacent over hypotenuse.
$\cos(45^\circ) = \frac{x}{1}$
We know $\cos(45^\circ) = \frac{\sqrt{2}}{2}$, so:
$x = \frac{\sqrt{2}}{2}$

Answer:

$\frac{\sqrt{2}}{2}$