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geometry obtuse triangle

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by kvcpk » Thu Jun 17, 2010 2:28 am
francoisph wrote:What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 1500?

any ideas please ?
i hope its not 1500 but 150. :)

Simple !!
formula is 1/2 * a* b* sinC
= 1/2 * 8 * 12 * sin150
=48 * sin30
=24

Let me know if you have any questions!!
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by francoisph » Thu Jun 17, 2010 2:32 am
yeah 150°

how to have the value Sin150?
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by kvcpk » Thu Jun 17, 2010 2:47 am
francoisph wrote:yeah 150°

how to have the value Sin150?
hmm.. Thats a tough question.. we will need to know the sin and cos values of 0,30,45,90,120,150,180,270,360

These will be useful when dealing with trigonometry..

you can see this link for reference..

https://www.analyzemath.com/trigonometry ... gles_1.gif
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by francoisph » Thu Jun 17, 2010 2:51 am
I cant believe that GMAT test us about sin and cos

I didnt do this stuff long years ago, it is nightmare
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by kvcpk » Thu Jun 17, 2010 3:03 am
francoisph wrote:I cant believe that GMAT test us about sin and cos

I didnt do this stuff long years ago, it is nightmare
Thats true.. But SIN and COS values for 30,45,60,90 would be sufficient enough.
I dont think we can do this problem without using any trigonometric functions..

I will post if i can find any way..
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by selango » Thu Jun 17, 2010 3:13 am
francoisph,

IMHO GMAT wont test trigonometric function.Usually geometry prob can be solved by using basic formulas.

What is the source of this question
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by jube » Thu Jun 17, 2010 4:25 am
Hey, while you don't need to remember any formula, I'm not sure either how you can solve this without a basic knowledge of trignometry.

IMO you do need to know the value of sin 30 & a basic understanding of what sin, cos and tan are for this sum.

Image

If you look at the figure I've attached, let the red line be p. Then: sin 30 = 8/p. Therefore p=4.

Hence area will be 1/2 * b * h = 1/2 * 12*8 = 24
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by Rich@VeritasPrep » Thu Jun 17, 2010 4:35 am
jube's got it!

You guys are correct: the GMAT does not test trig functions. However, this question can be solved without trig, as jube pointed out.

All you need to know is the proportions of a 30-60-90 triangle (which is DEFINITELY tested on the GMAT). The proportion is:

x : x*sqrt(3) : 2x. That's for the sides opposite the 30-, 60-, and 90-degree angles, respectively.

Notice that this means the hypotenuse is twice the length of the shortest side. So the imaginary triangle in jube's figure is a 30-60-90 triangle with a hypotenuse of 8 and a height of 4 (since the chosen height is opposite the 30-degree angle).

That height is the same height of the obtuse triangle. So for the obtuse triangle, base is 12 and height is 4, making for an area of 12*4 / 2 or 24.
Rich Zwelling
GMAT Instructor, Veritas Prep
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