Question

find the missing variables

Answer 1

The triangle on the image is a right triangle which means we can use trigonometry to untangle its mysteries.

We have a side an and angle from that we can compute anything.

We will first compute x, we do so by taking the cosine of an angle,

$\cos(45)=\frac{5\sqrt{2}}{x}$

$x=\frac{5\sqrt{2}}{\cos(45)}=\frac{5\sqrt{2}}{\frac{\sqrt{2}}{2}}=\frac{10\sqrt{2}}{\sqrt{2}}=\boxed{10}$

Then we can also compute y, simply by using pythagorean theorem,

$10^2=y^2+(5\sqrt{2})^2$

$y=\pm\sqrt{100-50}=\pm\sqrt{50}=\boxed{5\sqrt{2}}$.

So triangle has sides $5\sqrt{2},5\sqrt{2},10$ which is also known as equilateral triangle.

Hope this helps :)