Question

A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is `(pi)/12` and the angle between B and C is `(2pi)/3`. What is the area of the triangle?

Answer 1

Given measurements do not obey the Greater Angle and Greater Side theorem. Hence triangle cannot be formed.

Explanation:

`a = 8, b = 7, hatB = pi/12, hat A = (2pi)/3`

To find area of the triangle.

`color(brown)("As per the Greater Angle and Greater Side theorem"`

`color(crimson)(a > b " since" hat A > hat B`

`color(red)(a < b " though " hat A > hat B`

Hence cannot form a triangle with the given measurements.