Asked by Tommy
in triangle abc, if
sin c= (sin a + sin b )/ ( cos a + cos b )
prove that triangle abc is a right-angle triangle.
sin c= (sin a + sin b )/ ( cos a + cos b )
prove that triangle abc is a right-angle triangle.
Answers
Answered by
drwls
In a right triangle, assuming a and b are the acute angles, then a + b = 90 degrees and sin b = cos a, and sin a = cos b. Therefore
sin c = (sin a + sin b/(cos a + cos b)
= (cos a + cos b)/(cos a + cos b) = 1
Therefore c is a right angle. This proves that the relation is true for right triangles, if c is the right angle, but does not prove it is not true for other triangles.
sin c = (sin a + sin b/(cos a + cos b)
= (cos a + cos b)/(cos a + cos b) = 1
Therefore c is a right angle. This proves that the relation is true for right triangles, if c is the right angle, but does not prove it is not true for other triangles.
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