Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.

See classes
Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

Newsweek Readers’ Choice Awards 2026 winner: Target Test Prep, #1 Test Prep

Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.

★★★★★5.0563 reviews
GMATLiveTeachStarts Nov 22
Josh Braslow, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Josh Braslow, 20+ years in test prep

Nov 22 · Josh Braslow
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemandStart anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

EXECUTIVE ASSESSMENT

with

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemandStart anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 563 reviewsTarget Test Prep

m12, #6

Expert replies
Post new topic Post Reply
Subscribe topic
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 279
Joined: Fri Nov 05, 2010 5:43 pmFollowed by: 1 member
Thanked: 15 times
by mehrasa » Tue Jan 11, 2011 7:04 am
If in a right triangle, the ratio of the shortest side to the longest is [m]\frac{1}{2}[/m] , what is the smallest angle in this triangle?
Ans:30

I can not understand why the answer is.
As I know in the triangle, the shortest side is opposite smallest angle and vice verse.. when it is said it is right triangle so the largest angle is 90 and the largest side is diagonal.. here the ratio of smallest to largest is 1/2 so the '2' refer to diagonal which is 90 degree therefore, the smallest is 45 degree.

any further explanation?
Top
Join the discussion
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Tue Jan 11, 2011 7:26 am
This can be easily proved by trigonometry. The information given is equivalent to saying that sine of the smallest angle is equal to 1/2. Which is only possible if the measure of smallest angle is 30 degrees.


We can also conclude this using the famous property of '30-60-90' triangles. Which can be shown as follows.

Image

Refer to the figure above.

Largest side = c and smallest side = a
Thus, (a/c) = 1/2 => c = 2a

Again, (a² + b²) = c² = (2a)² = 4a²
=> b² = 3a²
=> b = (√3)a

Therefore ratio of the three sides of the triangle is a : b : c = a : (√3)a : 2a = 1:√3:2
The ratio of the lengths of three sides of a right-angled triangle is 1:√3:2, only when the triangle is 30-60-90 triangle. Hence the measure of the smallest angle is 30 degrees.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members
Thanked: 127 times

by Night reader » Tue Jan 11, 2011 7:33 am
the longest side is hypotenuse, as such two sides would be non-hypotenuse. The shortest side is always opposite the smallest interior angle. Of the two non-hypotenuse sides the shortest one would be opposite to hypotenuse. The ratio is 1/2 OR non-hypotenuse/hypotenuse. This is relationship 30`-60`-90` or 30` opposite to the shortest side.
Top
Join the discussion