Question

I need help trying to find side c and to see if my other answers are correct?

Answer 1

we have that

B=5 degrees

C=125 degrees

b=200 units

step 1

Find out the measure of angle A

Remember that

the sum of the interior angles in any triangle must be equal to 180 degrees

so

A+B+C=180

substitute given values

A+5+125=180

A=180-130

A=50 degrees

step 2

Applying the law of sines

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Find out the value of a

$\frac{\sin A}{a}=\frac{\sin B}{b}$

substitute given values

$\frac{\sin 50^o}{a}=\frac{\sin 5^o}{200}$

solve for a

$a=\frac{200\cdot\sin 50^o}{\sin 5^o}$

a=1,757.9 units

step 3

Find out the value of c

$\frac{\sin B}{b}=\frac{\sin C}{c}$

substitute given values

$\frac{\sin 5^o}{200}=\frac{\sin 125^o}{c}$$c=\frac{200\cdot\sin 125^o}{\sin 5^o}$

c=1,879.7 units