A triangle has sides A, B, and C. The angle between sides A and B is #pi/12# and the angle between sides B and C is #pi/12#. If side B has a length of 17, what is the area of the triangle?

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Answer 1 · 2017-09-30T12:03:22

The area of the triangle is #19.36# sq.unit [Ans]

The angle between sides # A and B# is #/_c=pi/12=180/12=15^0#

Angle between sides # B and C# is #/_a=pi/12=180/12=15^0#

Angle between sides # C and A# is #/_b=(180-(15+15)=150^0#

The Law of Sines (or Sine Rule) is:# A/sin a = B/sin b = C/sin c#

# B=17 :. A/sin a = B/sin b or A /sin15 = 17/sin150 # or

#A = 17* sin15/sin150 ~~ 8.8# So the sides #A and B# and their

included angle are #A=8.8 , B=17 and /_c =15^0#

The area of triangle is #A_t= (A*B*sinc)/2 =(8.8*17*sin15)/2# or

#A_t ~~19.36# sq.unit [Ans]