Name: Bryant

Who is asking: Other
Level: Secondary

The question that I am pondering is that I need to derive the law of cosines for a case in which angle C is an obtuse angle.

c 2 = a 2 + b 2 - 2ab cos C

cos(180 degrees - C) = -cos C


In the diagram below of a triangle with angle C obtuse, I extended the line segment BC drew a perpendicular from A to meet this extended line at D. Let x be the length of CD and h the length of AD.

Triangle ABD is a right triangle and hence

c 2

= (a + x) 2 + h 2

= a 2 + 2ax + x 2 + h 2
Triangle ACD is also a right triangle and thus b 2 = x 2 + h 2 Hence c 2

= a 2 + b 2 +2ax

Can you complete the proof?


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