How do you solve the triangle given α = 22 degrees, β = 115 degrees, and c = 12.75?

Question

1582 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-29T07:48:16

$gamma=43°$

$b~=16.94$

$a~=7$

Since the sum of the angles

$alpha+beta+gamma=180°$ ,

you simply can get $gamma=180°-22°-115°=43°$

Then you can use the sine theorem:

$a/sinalpha=b/sinbeta=c/singamma$

and find

$b=(csinbeta)/singamma$

$b=(12.75*sin115°)/(sin43°)$

$b~=16.94$

and

$a=(csinalpha)/singamma$

$a=(12.75*sin22°)/(sin43°)$

$a~=7$