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
Alan P.
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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