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04 Mar 2013, 00:13
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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.
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.
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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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04 Mar 2013, 00:47
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randomalgo
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.
04 Mar 2013, 00:52
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Thanks Vinay for the answer, you got the question right. but Isn't Sine Rule applicable only to right angle triangles? In that case, you assumed that one angle is 90 degree and applied the rule only to find out which one.
