Applications Of Derivatives Question 302
Question: If two sides of a triangle be given, then the area of the triangle will be maximum if the angle between the given sides be
Options:
A) $ \frac{\pi }{3} $
B) $ \frac{\pi }{4} $
C) $ \frac{\pi }{6} $
D) $ \frac{\pi }{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
Let a and b are given, then area $ A=\frac{1}{2}ab\sin C $
$ \Rightarrow \frac{dA}{dC}=\frac{1}{2}ab\cos C $
Hence A is maximum, when $ \frac{dA}{dC}=0\Rightarrow C=90{}^\circ $ .
BETA
