# How do you find the area of the triangle given A=43^circ45', b=57, c=85?

Feb 6, 2018

Area of triangle is $1675.16$ units.

#### Explanation:

When two sides and included angles are given,

area of triangle is half the product of the two sides multplued by sine ratio of included angle.

In a triangle sides are described as $a , b$ and $c$ and included angles as $A , B$ and $C$, as described in image below.

Therefore area is $\frac{1}{2} a b \sin C$ or $\frac{1}{2} b c \sin A$ or $\frac{1}{2} c a \sin B$

Here weare given $b = 57$, $c = 85$ and $A = {43}^{\circ} 45 ' = {43.75}^{\circ}$

Hence area is $\frac{1}{2} \times 57 \times 85 \times \sin {43.75}^{\circ}$

= $\frac{1}{2} \times 57 \times 85 \times 0.6915$

= $1675.16$ units