# How do you find the area of a triangle given A=18*, B=35*, c=3.4?

May 25, 2018

color(purple)(A_t = 3.31 sq units

#### Explanation:

$\hat{A} = {18}^{\circ} , \hat{B} = {35}^{\circ} , c = 3.4$

$\hat{C} = \left(180 - 18 - 35\right) = {127}^{\circ}$

As per Law of Sines,

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

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

$b = \frac{3.4 \cdot \sin 35}{\sin} 127 = 2.44$

Area of triangle -${A}_{t} = \left(\frac{1}{2}\right) b c \sin A$

${A}_{t} = \left(\frac{1}{2}\right) \cdot 2.44 \cdot 3.4 \cdot \sin \left(127\right)$

color(purple)(A_t = 3.31 sq units