Triangle Rules vs Sines and Cosines

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freiter1: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Apr 06, 2015 4:23 pm

by freiter1 » Fri Apr 17, 2015 6:34 pm

The 30-60-90 and isosceles triangle rules regarding side ratios are difficult for me to remember...

I did undergraduate and graduate school in engineering (7+years) thinking of triangles in terms of sines and cosines. Since the angles on the gmat are either 30, 45, 60, or 90, I can easily compute the sine or cosine of an angle in my head. It's 5x times faster for me to just take the sines and cosines of the angles in my head and work from there and I'm much more confident in my answer. As oppossed to when I use the triangle rule where I'm second guessing if I remembered the rule correctly or not and then I usually end up taking sines and cosines to check my answer anyways.

Are there any potential problems with me tossing out triangle side ratio rules from my memory? Or can I just stick with sines and cosines.

I know this must sound crazy to most people, but I've been doing it this way for so long and I also do it on a regular basis in my day-to-day job.

Any feedback is appreciated.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Apr 18, 2015 2:17 pm

freiter1 wrote:The 30-60-90 and isosceles triangle rules regarding side ratios are difficult for me to remember...

I did undergraduate and graduate school in engineering (7+years) thinking of triangles in terms of sines and cosines. Since the angles on the gmat are either 30, 45, 60, or 90, I can easily compute the sine or cosine of an angle in my head. It's 5x times faster for me to just take the sines and cosines of the angles in my head and work from there and I'm much more confident in my answer. As oppossed to when I use the triangle rule where I'm second guessing if I remembered the rule correctly or not and then I usually end up taking sines and cosines to check my answer anyways.

Are there any potential problems with me tossing out triangle side ratio rules from my memory? Or can I just stick with sines and cosines.

I know this must sound crazy to most people, but I've been doing it this way for so long and I also do it on a regular basis in my day-to-day job.

Any feedback is appreciated.

Hi freiter1,

Can you give us a specific example of what you're talking about?
In general, it's important to know the various ratios of the special right triangles (30-60-90 and 45-45-90), because, in most cases, the answer choices are exact.

Here's a very basic example: let's say we have an isosceles right triangle (ie, a 45-45-90 triangle), and one of the legs has length 1. What's the hypotenuse?
Using the ratios of the special right triangles, we quickly know that the length of the hypotenuse = âˆš2
You may know (from engineering) that sin45 â‰ˆ 0.707, so, the length of the hypotenuse = 1/0.707
If you recognize that 1/0.707 â‰ˆ âˆš2, that's great. Otherwise, you'll be in trouble.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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freiter1: Junior | Next Rank: 30 Posts; Posts: 10; Joined: Mon Apr 06, 2015 4:23 pm

by freiter1 » Sat Apr 18, 2015 5:36 pm

Hi Brent thanks for the response.

I tend to work sines and cosines in terms of square roots. Fair point if I saw 1/0.707 I wouldn't recognize that as 1/sqrt(2) while under pressure.

I learned that Sines and cosines of an angle are as easy as 1-2-3,3-2-1 just make this chart

30 ; 45; 60
Sin 1 ; 2 ; 3
Cos 3 ; 2 ; 1

Next you take square root and divide by 2

30 ; 45 ; 60
Sin 1/2 ; sqrt(2)/2 ; sqrt(3)/2
Cos sqrt(3)/2 ; sqrt(2)/2 ; 1/2

As an example problem from the OG for GMAT PS #92. I found it easier to say sin 60 = sqrt(3)/2 =opp/hyp.

so opp= 70*sqrt(3)/2=35*sqrt(3). Then the problem saysthe base of the ladder is 7ft above groung so final answer. 35*sqrt(3)+7 or letter D.

In other words when I'm taking a sine or cosine of angle, I'm really just counting 1-2-3 or 3-2-1, depending if I want sine or cosine.

I know this unconventional but are there any pitfalls you see with this approach?

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GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Apr 18, 2015 7:43 pm

I think test-takers need to work to their strengths.
If that approach quickly gets you to the correct answer, then that's the best approach (for you).

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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