# In triangle ABC, a = 7, A = 30 degrees, B = 70 degrees, What is angle C and length of side c?

Apr 26, 2017

hat C=80°
$c \cong 13.79$

#### Explanation:

Since the sum of the angles in a triangle is 180°, the angle C is :

hat C=180°-30°-70°=80°

You could get the length of side c by applying the sine theorem:

$\frac{a}{\sin} \hat{A} = \frac{c}{\sin} \hat{C}$

Then c=(a *sin hat C)/ sin hat A=(7*sin 80°)/(sin 30°)~=13.79

Apr 26, 2017

$C = {80}^{\circ}$

$c \approx 13.72$

#### Explanation:

The sum of the three angles of a triangle is ${180}^{\circ}$

So,

$\rightarrow C = {180}^{\circ} - {\left(70 + 30\right)}^{\circ}$

color(green)(rArrC=80^circ

To find the length of side $c$, use the sine theorem

color(brown)((a)/(sin(A))=(b)/(sin(B))=(c)/(sin(C) )

Let's use

color(purple)((a)/(sin(A))=(c)/(sin(C) )

$\rightarrow \frac{7}{\sin \left(30\right)} = \frac{c}{\sin \left(80\right)}$

$\rightarrow \frac{7}{\frac{1}{2}} = \frac{c}{0.98}$

$\rightarrow 14 \cdot 0.98 = c$

color(green)(rArrc~~13.72