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
Jim G.
Aug 5, 2017

"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"

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