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if I have a triangle ABC

sinA - 2sinBcosC = 0

Using the given information, what are some details/characteristics about triangle ABC? (if it's a right triangle/equilateral/what the angles are, etc.) 

any help is appreciated :)

 Mar 22, 2019
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it is a right isosceles triangle.  Notice the formula is the same as the double angle formula sin(2x) = 2sin(x)cos(x).  Here 2x = A and x = B = C.  Without proof I show that sin(90) - 2sin(45)cos(45) = 0 since 1 -2(1/sqrt2)(1/sqrt2) = 0.

 

But a proof shows that it does not have to be a right triangle -- just any isosceles triangle

 

sinA = 2sinBcosC

sinA = sin(180 -(B + C)) = sin(B + C)

sinA = sinBcosC + cosBsinC

2sinBcosC = sinBcosC + cosBsinC

simplifying

sinBcosC = cosBsinC

sinB/cosB = sinC/cosC

tanB = tanC

B = C

the triangle is isosceles

 Mar 22, 2019
edited by Guest  Mar 22, 2019

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