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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 #(5pi)/24# and the angle between B and C is # (7pi)/24#. What is the area of the triangle?

1 Answer

Dec 9, 2015

Area #triangle ABC = 7#

Explanation:

If #/_(C:A) =(5pi)/24#
and
#/_(B:C) = (7pi)/24#

then
#color(white)("XXX")/_(A:B) = pi - ((5pi)/24+(7pi)/24)#

#color(white)("XXXXXXXX")=pi-(12pi)/24 = pi/2#

i.e. #/_(A:B)# is a right angle
enter image source here

Treating #A# as the base and #B# as the height:

#color(white)("XXX")Area = 1/2xxbasexxheight = 1/2xx7xx2 = 7#

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