# How can an isosceles triangle have a right angle?

If the other two angles are ${45}^{\circ}$ each.
There's only one solution to $A = {90}^{\circ}$, $\quad B = C \quad$ and $A + B + C = {180}^{\circ}$ and that's $B = C = {45}^{\circ}$, so the ${45}^{\circ} , {45}^{\circ} , {90}^{\circ}$ right triangle is isosceles too.
If people's homework are any indication, you'll spend a whole year of trig studying the ${45}^{\circ} , {45}^{\circ} , {90}^{\circ}$ triangle and the ${30}^{\circ} , {60}^{\circ} , {90}^{\circ}$ triangle.