In this problem we are given a right triangle with 45 degree angle. We know that the sum of a triangle's angles needs to be equal to 180 degrees.
When we subtract 90+45 from 180 we got 45. That means we have an isoceles triangle.
According to the Pythagorean Theorem, [tex] a^{2} +b^{2} =c^{2} [/tex] .
When we plug in the numbers we get: [tex] a^{2} +b^{2} =10^{2} [/tex]
Because we know that a = b, we can write this as:[tex] a^{2} +a^{2} =10^{2} [/tex] or [tex] 2a^{2} =10^{2} [/tex]
Simplify: [tex] \frac{2a^{2}}{2} =\frac{100}{2} [/tex], then [tex] a^{2} =50 [/tex]
Take the square root: [tex] \sqrt{a^{2}} =\sqrt{50} =>a=5\sqrt{2} [/tex]
So, B is [tex] 5\sqrt{2} [/tex]
To find it faster we have a formula for this: "If a right triangle has 2 equal angles, the hypotenuse is equal to [tex] \sqrt{2} [/tex] times the leg."
Vice-versa: leg × [tex] \sqrt{2} [/tex] = hypotenuse or leg = hypotenuse / [tex] \sqrt{2} [/tex]
