# 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?

Apr 1, 2018

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

#### Explanation:

$a = 8 , b = 7 , \hat{B} = \frac{\pi}{12} , \hat{A} = \frac{2 \pi}{3}$

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.