Stan and Olga are considering buying a sheep farm. A surveyor has supplied them with the given accurate sketch. Find the area of the property

Question

Power · Answer

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Not to scale

Moon · Answer

yikes. not 100% sure on this but you could start by using law of cosines to find the missing sides, then using Heron's formula for the areas :S

Power · Answer

What I tried to do: (Find area of left triangle)
$\large {A=\frac{1}{2}sq}SinP$

$A=\frac12(8)(10)Sin(70º)$
$A=45.10$

$A=\frac12(s)(r)Sin(30º)$

Power · Answer

That second one I am stuck on

Power · Answer

Oh

Power · Answer

$p^2=s^2+q^2-2sqCos(P)$
$p^2=8^2+12^2-2(8)(12)Cos(70)$
$p^2=142.33$ (Approximately)
$p=11.93$?

Power · Answer

Oh wow I got it now, thanks!