A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 10, respectively. The angle between A and C is #(pi)/8# and the angle between B and C is # (3pi)/8#. What is the area of the triangle?

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Answer 1 · 2017-01-07T21:50:17

#S=35#

If #A/_C = pi/8# and #B/_C = (3pi)/8# then as the sum of the internal angles of a triangle always equals #pi#, we have:

#A/_B = pi-pi/8-(3pi)/8 = pi-(4pi)/8 = pi-pi/2 = pi/2#

Thus this is a right triangle where #A# and #B# are the legs, and #C# is the hypotenuse.

So the area of the triangle is:

#S = (A*B)/2 = (7*10)/2 = 70/2 = 35#