Question

suppose a triangle has two sides of lengths a and b. if the angle between these sides varies, what is the maximum possible area that the triangle can attain? what can you say about the minimum possible area? could you explain by detail

Answer 1

I did this for you yesterday
http://www.jiskha.com/display.cgi?id=1317265480

I used Calculus to answer the question, clearly the best and easiest way to do the question.

Are you not studying Calculus?

Answer 2

pre-calculus and i didn't understand where the d and cos came from

Answer 3

Ok, draw your base b
Now sketch the other side a , as the height.
You know that the area of the triangle is (1/2)(b)(a)
that is, the multiplication of ab must be as large as possible.
Since the base is fixed, the value of ab would be a maximum when the side 'a' is a vertical line, would you agree with that?
And of course a vertical line suggests an angle of 90° between them

Answer 4

thank you so much for all your help. i understood it now!