Hello!
To find side b of this right triangle, you would need to use cosine.
The formula for cosine is opposite / hypotenuse.
Since this is a 45-45-90 triangle, this type of triangle has unique characteristics compared to other triangles.
The ratio between the angles 45-45-90 are 1:1:√2. (or x : x : x√2).
45 → x, 90 → x√2
The given ratio says that the other sides of the triangle should be equal to half the hypotenuse times the √2.
. 5√2 is equal to about 7.071678...
We can check this method by using cosine.
cos(45) = b / 10 (multiply both sides by 10)
10cos(45) = b
b = 7.071678...
Therefore, the measure of side b is equal to 5√2.