Question

draw a triangle ABC in which AB:AC is 1:3 and BC 6 cm and angle c=75

Answer 1

No such triangle can exist
Proof:

let AB=x, then AC=3x
by the cosine law,
x^2 = 9x^2+36-2(6)(3x)cos75
8x^2 - 9.32x + 36 = 0

for which b^2-4ac= -165.14

Thus there are no real values possible for x