1. ## Sine rule!

Hi I have a question about one exercise. (See Atachment!) I do not get it how I have to calculate it.

Could someone help me?

a b c
-- --- ----
SinA SinB SinC

a b 34
---- ---- -----
sin45 sin60 SinC and now?

2. Originally Posted by Justin12
Hi I have a question about one exercise. (See Atachment!) I do not get it how I have to calculate it.

Could someone help me?

a b c
-- --- ----
SinA SinB SinC

a b 34
---- ---- -----
sin45 sin60 SinC and now?
$\displaystyle \frac {sinA}{a} = \frac {sinB}{b} = \frac {sinC}{c}$

$\displaystyle \frac {sin45}{a} = \frac {sin60}{b} = \frac {sinC}{34}$

You know that C = 75° (180° - 45° - 60°, which is the sum of all angles in a triangle (180°) minus the two angles you have)

$\displaystyle \frac {sin45}{a} = \frac {sin60}{b} = \frac {sin75}{34}$

Rest is simple algebra. If you still need help simplifying, tell me.

3. Just in case, before I leave, I'll post the answer as a spoiler, if you want to verify your equations and/or your answer.
Spoiler:

$\displaystyle \frac {sin45}{a} = \frac {sin60}{b} = \frac {sin75}{34}$

$\displaystyle \frac {sin45}{a} = \frac {sin60}{b} \approx 0,0284$

$\displaystyle \frac {sin45}{a} \approx 0,0284$

$\displaystyle a = \frac {sin45}{0,0284}$

$\displaystyle a \approx 24.89$

$\displaystyle \frac {sin60}{b} \approx 0,0284$

$\displaystyle b = \frac {sin60}{0,0284}$

$\displaystyle b \approx 30.49$