The area of a triangle is $A=\frac{1}{2}a*b*sin(c)$
$** sin( )$, where $a$, $b$ are two sides of the triangle and $c$ is the included angle. In surveying a triangular plot of land, $a$ and $b$ are $200ft$ and $150ft$ respectively, $c = 60°$ . By how much (approximately) is the computed area in error if a and b are in error by $0.5ft$ each and $c$ is in error by $2°$?
.............................................................
We know that our function is this:-$$A=\frac{1}{2}*a*b*sin(c)$$ and we have: $$a=200ft;b=150ft;c=60°$$ $$da=db=0.5ft;dc=2°$$ and we can find $dA$ with this:- $$dA=\frac{\partial{A}}{\partial{a}}da+\frac{\partial{A}}{\partial{b}}db+\frac{\partial{A}}{\partial{c}}dc$$
and I got: $$\frac{\partial{A}}{\partial{a}}=\frac{1}{2}*b*sin(c)$$ $$\frac{\partial{A}}{\partial{b}}=\frac{1}{2}*a*sin(c)$$ $$\frac{\partial{A}}{\partial{c}}=\frac{1}{2}*a*b*cos(c)$$
in my textbook, it says the answer is $(337.5ft^2)$, but when I substitute the values I don't get the same answer, why? and what am I doing wrong?