Expert: Abe Mantell - 8/22/2010

Question
two sides of triangle have length a and b and the angle between them i s 'x'. what value of 'x' will maximize the area of triangle?

Answer
Hello Akash,

Two ways to anwer this.

1. common sense: Since the area is (1/2)(base)(height),
.  if we let one of the legs be the base (let's say "b"),
.  then the maximum height will be when the angle between
.  side "a" and "b" are 90 degrees.

2. area formula: area=a*b*sin(x)
.  the sine function has a maximum value of 1 when
.  the angle,x, is 90 degrees.

Either way, we get 90 degrees.

Abe