Radian measure

[jinx24]

Hi all! I need a little help with this problem.

"Two angles in a triangle have radian measure pi/5 and pi/6. What is the radian measure of the third angle."

I know that the "radian measure" is the arc length / radius. But that does not really get me anywhere.

I don't know where to start. The only thing that I have done is convert the two radians into degrees, but I didn't get anywhere with that.

Thank you.
Jenny

 

[stapel]

What is the angle-sum of any triangle?

Eliz.

 

[jinx24]

Thank you. I guess I was on the right track by converting into degrees.

 

[soroban]

Hello, Jenny!

You're making hard work out of a simple problem.
$\displaystyle \;\;$And you don't have to convert to degrees.

Two angles in a triangle have radian measure $\displaystyle \frac{\pi}{5}$ and $\displaystyle \frac{\pi}{6}$.
What is the radian measure of the third angle.

We know that the sum of the angles of a triangle is: $\displaystyle 180^o$ or $\displaystyle \pi$ radians.

If two of the angles are $\displaystyle \frac{\pi}{5}$ and $\displaystyle \frac{\pi}{6}$,
$\displaystyle \;\;$the third angle is: $\displaystyle \,\pi\,-\,\frac{\pi}{5}\,-\,\frac{\pi}{6}\;=\;\left(1\,-\,\frac{1}{5}\,-\,\frac{1}{6}\right)\pi\;=\;\frac{19\pi}{30}$ radians.