# Thread: solve the triangle/with given parts

1. ## solve the triangle/with given parts

alpha=42.5degree
beta=35.2degree
a=18.0

2. Originally Posted by colie2020
alpha=42.5degree
beta=35.2degree
a=18.0
$\alpha + \beta + \gamma = 180^\circ$

find $\gamma$ , then use the sine law.

3. Originally Posted by colie2020
alpha=42.5degree
beta=35.2degree
a=18.0
I'm assuming side A is directly opposite angle $\alpha$, there is a side B opposite angle $\beta$, and there is a hypotenuse opposite angle $\gamma$.

If so...

The sum of the interior angles in a triangle equals 180, so:
$
\alpha + \beta + \gamma = 180
$

$
42.5 + 35.2 + \gamma = 180
$

$
\gamma = 102.3
$

The Law of Sines:

$
\frac{18}{\sin (42.5)} = \frac{B}{\sin (35.2)}
$

$
B = \frac{18\sin (35.2)}{\sin (42.5)}
$

$
\frac{18}{\sin (42.5)} = \frac{C}{\sin (102.3)}
$

$
C = \frac{18\sin (102.3)}{\sin (42.5)}
$

Check out the wikipedia entry on the law of sines:
Law of sines - Wikipedia, the free encyclopedia

What this problem is asking is known as triangulation:
Triangulation - Wikipedia, the free encyclopedia