Problem Solving

Given the relationship which states that "Angles correspond to their opposite sides", is it correct to assume there is a proportional relationship between the ratios of angle to side-lenght and vice versa within a triangle?

for example, in triangle ABC, if we are given the lenght of side AB as 5 units and the angle opposite to side AB as 35 degrees, would it be correct to assume that within this triangle, if the angle opposite side BC is 70 degrees, then BC would equal 10 units?

Basically, is it possible to just establish a proportion such as 35/5 = 70/x with x being the lenght of side BC? And the opposite as well of course, establishing angle size based on side-lenght proportion.

Thank you

Unfortunatley, the answer is NO. I believe the sides will be in proportion, but not in equal proportion..
You can say that the side opposite to the largest angle will be the longest side and the side opposite to the shortest angle will be shortest side.

Let me give a small example:

assume a right angled triangle with 30-60-90
let the side opposite 30 be x.
then , we know that the ratio of sides in 30-60-90 triangle is 1:root(3):2

Hence, the side opposite to 90 is 2x and not the side opposite to 60.

So, there exists no such proportion for all triangles.. Geometry does not make our lives so easy

A triangle's complete informaton can be found if any of these three are given:
1. three side lengths
2. two sides and the angle between them
3. two angles and the side between them.

If you can find any of the three above, then you can find the complete triangle measurements.

Hope this helps!!

Praveen

Praveen,

Thanks for your help. I guess it was nothing more than a nice idea...
Time to stop dreaming about reinventing geometry and back to my books

jeremy8 wrote:Praveen,

Thanks for your help. I guess it was nothing more than a nice idea...
Time to stop dreaming about reinventing geometry and back to my books

Kewl

All triangles exhibit the following proportionality:

In triangle ABC:

length AB/sin(angle opposite AB) = length BC/sin(angle opposite BC) = length AC/sin(angle opposite AC).

This rule of proportionality is not tested on the GMAT, so you shouldn't worry about it. The GMAT does not ask questions for which a knowledge of trigonometry is needed.

GMATGuruNY wrote:All triangles exhibit the following proportionality:

In triangle ABC:

length AB/sin(angle opposite AB) = length BC/sin(angle opposite BC) = length AC/sin(angle opposite AC).

This rule of proportionality is not tested on the GMAT, so you shouldn't worry about it. The GMAT does not ask questions for which a knowledge of trigonometry is needed.

Thanks. Even though it is not tested on the GMAT, I'm really interested in that relationship and I'll definitely look into it more (after I take the test...)