Condition for a right angle triangle : GMAT Quantitative Section
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 12:29

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Condition for a right angle triangle

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Mar 2013
Posts: 6
Location: United States
GMAT 1: 740 Q50 V40
Followers: 0

Kudos [?]: 6 [0], given: 1

Condition for a right angle triangle [#permalink]

### Show Tags

03 Mar 2013, 23:13
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.
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 80

Kudos [?]: 1116 [1] , given: 136

Re: Condition for a right angle triangle [#permalink]

### Show Tags

03 Mar 2013, 23:47
1
KUDOS
randomalgo wrote:
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.
_________________
Intern
Joined: 03 Mar 2013
Posts: 6
Location: United States
GMAT 1: 740 Q50 V40
Followers: 0

Kudos [?]: 6 [0], given: 1

Re: Condition for a right angle triangle [#permalink]

### Show Tags

03 Mar 2013, 23:52
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.
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 80

Kudos [?]: 1116 [0], given: 136

Re: Condition for a right angle triangle [#permalink]

### Show Tags

04 Mar 2013, 00:04
randomalgo wrote:
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.

No. It is true for any valid triangle.
_________________
Re: Condition for a right angle triangle   [#permalink] 04 Mar 2013, 00:04
Similar topics Replies Last post
Similar
Topics:
right Triangle Theorem 5 15 Jul 2012, 18:30
1 Ratio between angles and sides in a right angle traingle. 11 02 May 2012, 08:32
1 Right angled triangle in a circle 3 07 Feb 2012, 12:09
Standard lengths of right triangles 4 28 Feb 2010, 03:33
3 In the diagram to the right, triangle ABC has a right angle 17 03 Jul 2008, 15:12
Display posts from previous: Sort by