Two sides of a triangle are given. If the area of the triangle is maximum, then the angle between the given…
Two sides of a triangle are given. If the area of the triangle is maximum, then the angle between the given sides is
$45^{\circ}$
$30^{\circ}$
$60^{\circ}$
$90^{\circ}$
Solution
Let $A B C$ be a triangle and sides $a, b$ and $c$ are $B C, A C$ and $A B$, respectively.
Area of $\triangle A B C=\frac{1}{2} a b \sin C$
Now, fixed value of $a$ and $b$ area of triangle is maximum when $\sin C=1$
$
\Rightarrow C=\frac{\pi}{2} \text { or } 90^{\circ}
$