Question

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

Answer 1

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 `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