How do you find the angles of a RIGHT triangle with only the three sides?

Question

anonymous · Answer

You can use trigonometry.

anonymous · Answer

|dw:1369768054295:dw|According to your problem, you are apparently given the measures of a, b, and c.  You can get the measures of the angles by various inverse trigonometric ratios:

B = Arcsin (b/a)

C = Arcsin (c/a)

Those are just 2 examples.  You can use Arctan and Arccos if you wanted to.

anonymous · Answer

I have tried that. The question I am doing is confusing.

anonymous · Answer

@tcarroll010 what is arcsin?

amistre64 · Answer

one idea is to use the law of cosine

amistre64 · Answer

but tangents are fine

anonymous · Answer

Arcsin = $$\sin^{-1} $$

anonymous · Answer

Ok, Let me try that quick!

anonymous · Answer

It's the angle you want and arcsin is:

"the angle whose sin is . . ."

It's the inverse of the sine

anonymous · Answer

I got it! Thank you soo much!

amistre64 · Answer

law of cosine would amount to
$$c^2=a^2+b^2-2ab~cos(C)$$
$$-\frac{c^2-(a^2+b^2)}{2ab}=~cos(C)$$
and inverse

anonymous · Answer

When you are looking for the measure of the length of a side, you usually use the trigonometric ratios, if you are using trigonometry at all.  If you want the angle, you use the *inverse* trigonometric ratios.

uw!

anonymous · Answer

Good luck to you in all of your studies and thx for the recognition! @shaylynnwalls1