If overline{PQ} and overline{PR} are two side | vedclass

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(D) Let $PQ = a$ and $PR = b$,and let $	heta$ be the angle between them.The area of $\Delta PQR$ is given by $A = \frac{1}{2} ab \sin 	heta$.Let $f(

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$\pi /2$

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(D) Let $PQ = a$ and $PR = b$,and let $	heta$ be the angle between them.The area of $\Delta PQR$ is given by $A = \frac{1}{2} ab \sin 	heta$.Let $f(	heta) = \frac{1}{2} ab \sin 	heta$.To find the maximum area,we differentiate $f(	heta)$ with respect to $	heta$:$f'(	heta) = \frac{1}{2} ab \cos 	heta$.For maximum area,set $f'(	heta) = 0$:$\frac{1}{2} ab \cos 	heta = 0 \implies \cos 	heta = 0$.Since $0 Using the second derivative test:$f''(	heta) = -\frac{1}{2} ab \sin 	heta$.At $	heta = \frac{\pi}{2}$,$f''(\frac{\pi}{2}) = -\frac{1}{2} ab Since the second derivative is negative,the area is maximum at $	heta = \frac{\pi}{2}$.

If $\overline{PQ}$ and $\overline{PR}$ are two sides of $\Delta PQR$,for what value of the angle between $\overline{PQ}$ and $\overline{PR}$ is the area of the triangle maximum?

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