Law of Sines

A

Aladdin

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Mar 27, 2009
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553
Assume there exist the following relation in triangle ABC: sinB= 2sinC.cosA

a) Prove That we also have the relation b = 2c.cosA .

My Work : Form the first relation I've just got the cosA and then replaced it in the second relation , But I think I've gone no where :!:

b) Deduce that the triangle is isosceles .

My Work: To prove a triangle is isosceles : the base angles should be equal or the two sides adjacent to the vertex must be equal :!:

Please I don't need answers I just need some hints or clarification .
Thank you
 
Aladdin said:
Assume there exist the following relation in triangle ABC: sinB= 2sinC.cosA

a) Prove That we also have the relation b = 2c.cosA .

My Work : Form the first relation I've just got the cosA and then replaced it in the second relation , But I think I've gone no where :!:

b) Deduce that the triangle is isosceles .

My Work: To prove a triangle is isosceles : the base angles should be equal or the two sides adjacent to the vertex must be equal :!:

Please I don't need answers I just need some hints or clarification .
Thank you
Click to expand...

From the Law of Sines, you know that

a/sin A = b/ sin B = c / sin C

Certainly any TWO of these fractions are equal to each other...choose the last two:

b / sin B = c / sin C

You're given that sin B = 2 sin C cos A. Subtitute (2 sin C cos A) for sin B:

b / (2 sin C cos A) = c / sin C

Multiply both sides of that equation by the common denominator of the two fractions......
 
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