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

Related questions
See all questions in Area of a Triangle
Impact of this question
1506 views around the world
You can reuse this answer
Creative Commons License