+160 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 :)
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
