I was just wondering...

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EddieU: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun May 22, 2011 4:53 amFollowed by: 1 member; Thanked: 1 times

by EddieU » Sat Jun 18, 2011 3:20 am

if it's possible to determine the length of a triangle with only the information of the inner degree...

eg. what is the length of the base AB when the two degrees CA and BC are 90 degrees and 35 degrees respectively?
(I did not choose the degrees 90 and 45 on purpose because that gives us the x-x-xsqrt2 lengths)

Thank you

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Source: Beat The GMAT — Problem Solving | Sat Jun 18, 2011 3:20 am

Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sat Jun 18, 2011 3:46 am

Hi,
We can only find the ratio of side lengths when the internal angles of the triangle are given.
Even, in your case of 90,45,45 you can only get ratio but not the absolute values.
The ratio of sides of a triangle is same as the ratio of the sine(angle opposite to side).

Cheers!

Things are not what they appear to be... nor are they otherwise

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EddieU: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Sun May 22, 2011 4:53 amFollowed by: 1 member; Thanked: 1 times

by EddieU » Sat Jun 18, 2011 4:30 am

Frankenstein wrote:Hi,
We can only find the ratio of side lengths when the internal angles of the triangle are given.
Even, in your case of 90,45,45 you can only get ratio but not the absolute values.
The ratio of sides of a triangle is same as the ratio of the sine(angle opposite to side).

Thanks for the quick reply,

could you please give me an example how to calculate the the ratios when you have the degrees 90, 35, 55

even with the triangle 90, 45, 45 I can't really see which one the opposite side is...there are always two opposite sides (opposite of 90degree are 45 and 45) I just know that 90 is double 45, so if 45 is x, 90 has to be 2x...but it would be nice to know how to get those ratios when the degrees differ from the standard 45-45-90 or 30-60-90 schema

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Frankenstein: Legendary Member; Posts: 1448; Joined: Tue May 17, 2011 9:55 amFollowed by: 53 members; Location: India; Thanked: 375 times

by Frankenstein » Sat Jun 18, 2011 4:40 am

Hi,
If ABC is a triangle, BC is the opposite side of vertex A
AC is the opposite side of vertex B
AB is the opposite side of vertex C

Now, if the angles A,B,C are 90,45,45 respectively,
then BC:AC:AB = sine(angleA):sine(angleB):sine(angleC) = sine 90 : sin45: sine45
= 1:1/sqrt2:1/sqrt2 = sqrt2:1:1

Similarly for the case of 90,35,55, the ratio of sides will be sine 90 : sin35: sine55. For this we need to know the sine values of 35 and 55 degrees.

Cheers!

Things are not what they appear to be... nor are they otherwise

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amit2k9: Master | Next Rank: 500 Posts; Posts: 461; Joined: Tue May 10, 2011 9:09 amFollowed by: 3 members; Location: pune; Thanked: 36 times

by amit2k9 » Sat Jun 18, 2011 5:51 am

with sin and cos 35 one can only get the ratio's of the sides not the actual measurements.
However, if one of the sides is known then it will help to determine the other sides.

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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 Jun 18, 2011 10:57 am

In case there are students out there thinking, "Sines! I need to know about sines?!", I thought I should jump in and mention that you do not need to know about sines, cosines and tangents on the GMAT.

If you are asked to find the length of the side in a triangle, you will need to apply the Pythagorean theorem, or your knowledge similar triangles or "Special" triangles (45-45-90 or 30-60-90)

The above discussion, while mathematically correct, is beyond the scope of the GMAT.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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