Triangle with 2 Sides

Keeping side of length 105 fixed, swivel the side of length 88 to maximum altitude, which happens when it's a right triangle. Use Pythagorean to find hypotenuse length of 137.

$We\ have\ sides\ 88\ and\ 105\ and\ let\ the\ angle\ between\ them\ be\ \theta ,$ $Area\ of\ triangle=\frac{1}{2}ab\cdot \sin \theta$ $A=\frac{1}{2}88\cdot 105\cdot \sin \theta$ $For\ area\ to\ be\ maximum\ \frac{dA}{d\theta }\ should\ be\ zero,$ $\frac{dA}{d\theta }=\frac{1}{2}88\cdot 105\cdot \cos \theta$ $\cos \theta =0$ $\theta =\frac{\pi }{2}$ $By\ pythagoras\ theorem,$ $88^2+105^2=\left(Other\ side\right)^2$ $Other\ side\ =137.$ @Pi Han Goh Look it.