Question

A triangle has sides A, B, and C. The angle between sides A and B is `(7pi)/12` and the angle between sides B and C is `pi/12`. If side B has a length of 26, what is the area of the triangle?

Answer 1

`"area "~~ 97.568" square units"`

Explanation:

`"calculate the area ( A ) of the triangle using"`

`•color(white)(x)A=1/2ABsinC`

`"where C is the angle between sides A and B"`

`"we require to calculate the side A"`

`" the third angle in the triangle is"`

`pi-((7pi)/12+pi/12)=pi/3`

`"using the "color(blue)"sine rule "`in triangle ABC

`A/sin(pi/12)=26/sin(pi/3)`

`rArrA=(26sin(pi/12))/(sin(pi/3))~~ 7.77`

`rArr"area( A)"=1/2xx7.77xx26xxsin((7pi)/12)`

`color(white)(rArrareaA)~~ 97.568" to 3 dec. places"`