Thread: trigonometry ABC triangle

of a ABC triangle
a=5 , b=4 and cos(A-B)=31/32

show that c=6

Hello, stud_02!

I found a solution . . . but there must be a better way!

In
Show that: .

Code:

              C
              *
             *| *
            * |   *
       b=4 *  |     * a=5
          *   |y      *
         *    |         *
        *     |           *
       *      |             *
    A * - - - * - - - - - - - * B
      :   x   D      c-x      :
      : - - - - - c - - - - - :

In right triangle .[1]

In right triangle .[2]

Equate [1] and [2]: . .[3]

Substitute into [1]: . .[4]


We are given: .

. . . .

Substitute [3] and [4]: .

. . which simplifies to: .