You get a bonus - 1 coin for daily activity. Now you have 1 coin

Sine Theorem

Lecture






Theorem

The sides of the triangle are proportional to the sines of the opposite angles.

  Sine Theorem

Evidence.

Let there be Δ ABC with sides a, b, c and angles α, β, γ.
Prove that

  Sine Theorem

We will carry out from CD height CD. Then from Δ ACD we get:

  Sine Theorem

If angle α is blunt, then

  Sine Theorem

From Δ BCD we get

  Sine Theorem

Similarly, we get

  Sine Theorem

The theorem is proved.
created: 2014-10-05
updated: 2021-03-13
132528



Rating 9 of 10. count vote: 2
Are you satisfied?:



Comments


To leave a comment
If you have any suggestion, idea, thanks or comment, feel free to write. We really value feedback and are glad to hear your opinion.
To reply

Planometry

Terms: Planometry