Question

A triangle has sides A, B, and C. Sides A and B have lengths of 10 and 5, respectively. The angle between A and C is `(5pi)/24` and the angle between B and C is `(pi)/24`. What is the area of the triangle?

Answer 1

`color(brown)("But in the given sum, " a > b " & " hat A < hat B`

`color(blue)("Hence such a triangle cannot exist."`

Explanation:

`a = 10, hat A = pi/24, b = 5, hat B = (5pi) / 24`

As per the Greater angle and Greater side theorem,

`color(indigo)(a > b " if and only if " hat A > hat B`

`color(brown)("But in the given sum, " a > b " & " hat A < hat B`

`color(blue)("Hence such a triangle cannot exist."`