How do you find a side of triangle given 3 angles?

Answer 1

The angles of a triangle don't change no matter how big or small the triangle is, so finding the length is impossible, but you can find the ratio of the triangle from this, as so:

-Set one side of the triangle equal to 1

-Use this information to solve (capital letters representing angles, lower-case representing sides)

A= 30 a= 1

B= 60 b=

C= 90 c=

see how side a equals one?

Next, you need to use the law of sines, which are as follows:

this may look complex, but it's really not, all you need is a calculator, and it's easy enough:

, so all you have to do is cross multiply (sin60*1, then divide that by sin30) and you should get 1.7, so:

A= 30 a= 1

B= 60 b= 1.7

C= 90 c=

then, you do the same to solve for c:

you should get 2

A= 30 a= 1

B= 60 b= 1.7

C= 90 c= 2

and here are the ratios for this triangle.

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The law of sines states that, for sides A, B, C and angles a,b,c across the sides respectively,

A/sin a = B/sin b = C/sin c

Use this to figure out the sides, or the ratio of the sides. Another interesting fact is that this ratio is also equal to 2R, where R is the radius of the circumscribed circle.