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Re: What is the area of an obtuse angled triangle whose two side [#permalink]

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09 Jul 2012, 20:56

ficklehead 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? A. 24 sq units B. 48 sq units C. 24*root3 D.48*root3 E. Such a triangle does not exist

Hi,

The shortcut method is to use the formula, area = 1/2*a*b*sinC =1/2*8*12*sin(150) =48*sin(30) =24

The longer method is:

Attachment:

tri.jpg [ 9.43 KiB | Viewed 10430 times ]

here, AB=8, AC = 12 & angleABC=150 Find the area of triangle ADC & triangle ADB area (ABC) = ADC - ADB

What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?

A. 24 sq units B. 48 sq units C. 24*root3 D. 48*root3 E. Such a triangle does not exist

Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, we are expected to solve this problem in the following way:

Attachment:

Triangle.png [ 12.95 KiB | Viewed 10392 times ]

Notice that triangle ABD is 30°-60°-90° right triangle. Now, in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).

Next, the area of triangle ABC equals to the area of triangle ACD minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).

Re: What is the area of an obtuse angled triangle whose two side [#permalink]

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10 Jul 2012, 02:35

1

This post received KUDOS

Bunuel wrote:

Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

Hi Bunuel,

I agree that some topics are out of scope of GMAT, but that doesn't mean one can't use it. It is always better to learn few advanced concepts (wrt GMAT) as it allows one to quickly find the answer. Our only struggle is with time in GMAT.

Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

Hi Bunuel,

I agree that some topics are out of scope of GMAT, but that doesn't mean one can't use it. It is always better to learn few advanced concepts (wrt GMAT) as it allows one to quickly find the answer.

Regards,

Who said that one cannot use trigonometry? Sure if you know trigonometry then you CAN use it. Again: trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, if you don't know trigonometry then you absolutely don't need to waste your time on it.
_________________

Re: What is the area of an obtuse angled triangle whose two side [#permalink]

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26 Jul 2012, 09:21

How do we know that AB=8, AC = 12? we are not given the third side. The third side can be between 4 and 20, so why not the side opposite to 150? be any number greater that 12 and less that 20?

Re: What is the area of an obtuse angled triangle whose two side [#permalink]

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27 Jul 2012, 04:00

ashwinkumar96 wrote:

How do we know that AB=8, AC = 12? we are not given the third side. The third side can be between 4 and 20, so why not the side opposite to 150? be any number greater that 12 and less that 20?

Well, Maybe its not worded properly. It also says the included angle is 150. So the 2 sides are 12 and 8.

Kudos me if you think I deserve it It helps!
_________________

I've failed over and over and over again in my life and that is why I succeed--Michael Jordan Kudos drives a person to better himself every single time. So Pls give it generously Wont give up till i hit a 700+

Re: What is the area of an obtuse angled triangle whose two side [#permalink]

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05 Dec 2012, 11:21

Can I ask if the image was part of the problem or if you've drawn it on your own? If you did how did you decide that AB = 8 and not 12? Brother Karamazov

Can I ask if the image was part of the problem or if you've drawn it on your own? If you did how did you decide that AB = 8 and not 12? Brother Karamazov

The figure was not attached to the problem. As for the sides: it doesn't matter which side we assign to be 8 or 12 (if you consider AB=12 and BC=8, you'll get the same answer).
_________________

Re: What is the area of an obtuse angled triangle whose two side [#permalink]

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15 Aug 2013, 01:39

Bunuel wrote:

ficklehead 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 150°?

A. 24 sq units B. 48 sq units C. 24*root3 D. 48*root3 E. Such a triangle does not exist

Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, we are expected to solve this problem in the following way:

Attachment:

Triangle.png

Notice that triangle ABD is 30°-60°-90° right triangle. Now, in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).

Next, the area of triangle ABC equals to the area of triangle ACD minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).

Answer: A.

.

I would like to make two quick points:

1. Once you have found out the height of the triangle (AD), which is 4 here, you could have found out the area of the required triangle(ABC) simply by multiplying half of the height AD (1/2*4) and base BC (12) instead of using such a long method of find the area of ACD and subtracting from it the area of ABD.

2. Its irrelevant whether one is memorizing/using this formula (\(1:\sqrt{3}:2\) ) or memorizing/using trigonometric tables ( Although I feel knowledge of basic trigonometry is more handy), as all these formulas are interrelated. I just feel that students should be given the choice between the two. Hence, such basic trigonometry should be included in the prep materials.

What is the area of an obtuse angled triangle whose two sides are 8 and 12 and the angle included between two sides is 150°?

A. 24 sq units B. 48 sq units C. 24*root3 D. 48*root3 E. Such a triangle does not exist

Note that trigonometry is not tested on the GMAT, which means that EVERY GMAT geometry question can be solved without it.

So, we are expected to solve this problem in the following way:

Attachment:

Triangle.png

Notice that triangle ABD is 30°-60°-90° right triangle. Now, in 30°-60°-90° right triangle the sides are always in the ratio \(1:\sqrt{3}:2\), hence hypotenuse AB=8 corresponds to 2 and therefore \(AD=\frac{8}{2}=4\) and \(DB=8*\frac{\sqrt{3}}{2}=4\sqrt{3}\).

Next, the area of triangle ABC equals to the area of triangle ACD minus the area od triangle ABD: \(area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24\).

Answer: A.

.

I would like to make two quick points:

1. Once you have found out the height of the triangle (AD), which is 4 here, you could have found out the area of the required triangle(ABC) simply by multiplying half of the height AD (1/2*4) and base BC (12) instead of using such a long method of find the area of ACD and subtracting from it the area of ABD.

2. Its irrelevant whether one is memorizing/using this formula (\(1:\sqrt{3}:2\) ) or memorizing/using trigonometric tables ( Although I feel knowledge of basic trigonometry is more handy), as all these formulas are interrelated. I just feel that students should be given the choice between the two. Hence, such basic trigonometry should be included in the prep materials.

Completely disagree.

30-60-90 and 45-45-90 triangles are "GMAT triangles", so everyone should know the relationship between their sides and not spend time going into trigonometry.
_________________

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