A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2# and the angle between sides B and C is #pi/12#. If side B has a length of 9, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2# and the angle between sides B and C is #pi/12#. If side B has a length of 9, what is the area of the triangle?

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Answer 1 · 2016-08-12T09:00:47

#=10.85#

Explanation:

Clearly this is a right-angled triangle where #base= B=9# and angle between #A# and #C# =#pi-(pi/2+pi/12)=pi-((7pi)/12)=(5pi)/12#
Therefore we can write
#B/A=tan((5pi)/12)#
or
#9/A=3.73#
or
#A=9/3.73#
or
#A=2.41# (Pl.note #A# is the #height#)
Area of the triangle #=1/2times height timesbase=1/2times2.41times9=10.85#

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A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/2# and the angle between sides B and C is #pi/12#. If side B has a length of 9, what is the area of the triangle?

1 Answer

Explanation:

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