If a triangle has an angle 30 degree and two other sides (Not the one making the angle) have lengths in the ratio of 1:2, is it a sufficient condition for the triangle to be right angle? (e.g. Triangle ABC has angle B = 30 degree and AC:BC = 1:2, Is it a sufficient condition for angle A to be 90 degree?)
It appears to be true, but I am unable to prove it with the knowledge of geometry I have. I have my GMAT approaching in 10 days. Would appreciate if someone could prove it at the soonest. Thanks.
Yes it is. The law of sines says :
a/sinA = b/sinB = c/sinC
Thus, here, we have 2x/sinA = x/sin30
or sinA = sin30*2 = 0.5*2 = 1.
Thus, A = 90 degrees.
I have assumed the triangle described by you in the query.
All that is equal and not-Deep Dive In-equality
Hit and Trial for Integral Solutions