# 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?

##### 1 Answer

Aug 5, 2017

#### 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"#