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Intern  Joined: 24 Jul 2011
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What is the area of an obtuse angled triangle whose two side  [#permalink]

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Question Stats: 37% (01:41) correct 63% (01:47) wrong based on 134 sessions

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

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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 16600 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: $$area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24$$.

For more check Triangles chapter of Math Book: math-triangles-87197.html

Hope it helps.
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Current Student B
Joined: 29 Mar 2012
Posts: 295
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GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

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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 16636 times ]

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

Regards,
Current Student B
Joined: 29 Mar 2012
Posts: 295
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

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1
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.

Regards,
Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

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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.

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

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

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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.

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Intern  Joined: 11 Jul 2012
Posts: 39
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

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

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

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Bunuel 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: $$area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24$$.

.

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.
Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Re: What is the area of an obtuse angled triangle whose two side  [#permalink]

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agourav wrote:
Bunuel 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: $$area=\frac{1}{2}*AD*DC-\frac{1}{2}*AD*DB=\frac{1}{2}*4*(4\sqrt{3}+12)-\frac{1}{2}*4\sqrt{3}=24$$.

.

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

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