Can Triangle Side Lengths be Determined from Angles Alone?

[PrudensOptimus]

I have here a standard 90 degree triangle.

_______B________
| /
| /
| /
| /
A /
| C
| /
| /
| /
| /
| /
| /
| /
| /
|/


I know not the numerical value of A,B,C. However, I do know all of the angles they are corresponding to respectively.

How can i find A...

 

[danne89]

What do you mean?. Do you know every angle in the triangle?

In that case:
sin A/a = sin B/b = sin C/c The law of sinus

 

[Curious3141]

Your diagram is difficult to interpret. A general rule is that knowing three angles of a triangle tells you nothing about the measure of their sides, since there are an infinite number of similar triangles.

You always need a minimum of 3 non trivial things to specify a plane triangle, either

a) two angles and one side.

b) two sides and one included angle.

Given a), you can find all the sides with the sine rule. The third angle can be found trivially by subtracting from the angle sum of 180 degrees. Given b), you can find the remaining side with the cosine rule, then use the sine rule to find one other angle, the third angle is trivial to find by subtraction.

 

[Zurtex]

Quote his text to see what his diagram was supposed to look like.

I believe if you know the length of all 3 sides you can also work out the angles. But always make sure the triangle follows the triangle equality.

 

[HallsofIvy]

If A is the length of the side, then it is impossible to find lengths knowing only angles. All "similar triangles" have the same angles no matter what the lengths are.

If you know that angles and ONE side length, then you can find the other lengths.

 

[PrudensOptimus]

What do you mean?. Do you know every angle in the triangle?

In that case:
sin A/a = sin B/b = sin C/c The law of sinus

Law of Sin won't work... i know not any of the sides.

 

[DaveC426913]

The lengths of the sides cannot be calculated

...UNLESS...

...you weren't asked for an actual measurement - you can supply a *proportion* (i.e. algebra):
The length of A in relation to B and C is ...
The length of B in relation to A and C is ...
The length of C in relation to A and B is ...

Example: if the AC and BC angles are 45 degrees, then:

$$A = B = \sqrt{\frac{1}{2} (C^2)}$$
$$C=\sqrt{A^2+B^2}$$
(But that's the easy triangle.)

 

[DeadWolfe]

Of course you can't calculate the sides!

Isn't it easy to visualize that if you took any given triangle, and simple stretched it every direction, it is quite possible to increase all the sides without changing the angles?