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

1 Answer
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.

Triangle not drawn to scale as given in question.

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