A triangle has sides A, B, and C. Sides A and B have lengths of 7 and 9, respectively. The angle between A and C is #(pi)/8# and the angle between B and C is # (pi)/24#. What is the area of the triangle?

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Answer 1 · 2018-04-07T09:52:35

#"Since " color(brown)(a / sin A != b / sin B), color(crimson)(" we can not form a triangle with the given measurements."#

As per the Law of Sines, #a / sin A = b / sin B#

#a / sin A = 7 / sin (pi/24) = 53.63#

#b / sin B = 9 / sin (pi/8) = 23.52#

#"Since " color(brown)(a / sin A != b / sin B), color(crimson)(" we can not form a triangle with the given measurements."#

Answer 2 · 2018-04-07T10:01:28

#color(purple)("Inconsistency in the given measurements according to the Greater Angle and Greater Side Theorem"#

#"As per the Greater Angle and Greater Side Theorem'"#

#b > a, "if and only if " hat B > hat A#

#"Since " hat B < hat A, " though " b > a, " we cannot form a triangle with the given measures."#