Triangles Similarity: small triangle w/ a=alpha, s1=20, s2=v; medium triangle w/ a=alpha, s=45, s=36; and...

[enji]

 

[MarkFL]

I would try using the Law of Sines, along with the identity for sines regarding supplemental angles.

 

[Dr.Peterson]

View attachment 35013

Do you know the Angle Bisector Theorem? That directly solves this.

If you can't use that, you can prove it, by thinking about the ratio of the areas of the two triangles.

 

[MarkFL]

Do you know the Angle Bisector Theorem? That directly solves this.

If you can't use that, you can prove it, by thinking about the ratio of the areas of the two triangles.

Yes, a friend of mine solved it in seconds using the angle bisector theorem. I guess I am a bit rusty. ?

 

[MarkFL]

The first proof of the angle bisector theorem given by Wikipedia uses the exact method I applied to this problem, so I don't feel too bad.