Question

How do you find the area of triangle ABC given `A=171^circ, B=1^circ, C=8^circ, b=2`?

Answer 1

Assuming that I didn't make any calculator mistakes:
`color(white)("XXX")"Area"_triangle~~2.494953309` sq.units

Explanation:

By the Law of Sines:
`color(white)("XXX")a/(sin(A))=b/(sin(B))=c/(sin(C))`

For the given values this means:
`color(white)("XXX")a=(sin(171^circ)*2)/(sin(1^circ))`

`color(white)("XXXx")~~17.92697937`

and
`color(white)("XXX")c=(sin(8^circ)*2)/(sin(1^circ)`

`color(white)("XXXx")~~15.94887232`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This gives a perimeter of
`color(white)("XXX")p=17.92697937+2+15.94887232`
`color(white)("XXXx")=35.87585168`
and a semi-perimeter of
`color(white)("XXX")s=35.87585168 div 2`
`color(white)("XXXx")=17.93792584`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using Heron's Formula for the Area of a Triangle
`color(white)("XXX")"Area"_triangle=sqrt(s(s-a)(s-b)(s-c))`

`color(white)("XXXXXXX")~~2.494953309`