Question

Geometry.Find the indicated side of the triangle. Include a clear answer and description if possible

Answer 1

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, $a^{2} +b^{2} =c^{2}$ .

When we plug in the numbers we get: $a^{2} +b^{2} =10^{2}$

Because we know that a = b, we can write this as:$a^{2} +a^{2} =10^{2}$ or $2a^{2} =10^{2}$

Simplify: $\frac{2a^{2}}{2} =\frac{100}{2}$, then $a^{2} =50$

Take the square root: $\sqrt{a^{2}} =\sqrt{50} =>a=5\sqrt{2}$

So, B is $5\sqrt{2}$

To find it faster we have a formula for this: "If a right triangle has 2 equal angles, the hypotenuse is equal to $\sqrt{2}$ times the leg."

Vice-versa: leg × $\sqrt{2}$ = hypotenuse or leg = hypotenuse / $\sqrt{2}$