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

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Answer 1 · 2018-02-06T14:51:18

Area of triangle is $1675.16$ units.

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.

![Triangle not drawn to scale as given in http://question.](https://useruploads.socratic.org/BDx5citJSfaSt1TgKaFj_triangle.png)

Therefore area is $1/2ab sinC$ or $1/2bcsinA$ or $1/2casinB$

Here weare given $b=57$ , $c=85$ and $A=43^@45'=43.75^@$

Hence area is $1/2xx57xx85xxsin43.75^@$

= $1/2xx57xx85xx0.6915$

= $1675.16$ units

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