A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 2, respectively. The angle between A and C is (11pi)/24 and the angle between B and C is (11pi)/24. What is the area of the triangle?

1 Answer
SagarStudy
Jan 15, 2016

First of all let me denote the sides with small letters a, b and c.
Let me name the angle between side a and b by /_ C, angle between side b and c by /_ A and angle between side c and a by /_ B.

Note:- the sign /_ is read as "angle".
We are given with /_B and /_A. We can calculate /_C by using the fact that the sum of any triangles' interior angels is pi radian.
implies /_A+/_B+/_C=pi
implies (11pi)/24+(11pi)/24+/_C=pi
implies/_C=pi-((11pi)/24+(11pi)/24)=pi-(11pi)/12=pi/12
implies /_C=pi/12

It is given that side a=7 and side b=2.

Area is also given by
Area=1/2a*bSin/_C

implies Area=1/2*7*2Sin(pi/12)=7*0.2588=1.8116 square units
implies Area=1.8116 square units

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