A terrain is triangular in shape. During a topographic study, 2 sides were measured, $x=150 \text{m}$ and $y=200\text{m}$ and the included angle between them was $60°$. If the study allows an error in the sides of $5\text{cms}$ and in the angle of $2°$ then what is the approximate error in calculating the triangle's area?
Im sorry, I don't speak English. I hope that you to understand me.
(Note: The language has been improved in an edit from the original version.)
This exercise is about using differential
I don't know how do this.
I think that:
$A=\frac{1}{2}\cdot x\cdot y\cdot\sin \theta$
$dA=\frac{1}{2}\cdot y\cdot\sin \theta\cdot dx+\frac{1}{2}\cdot x\cdot\sin \theta\cdot dy+\frac{1}{2}\cdot x\cdot y\cdot\cos \theta\cdot d\theta$
$dA=0.5\cdot 200\cdot 0.05+0.5\cdot150\cdot0.05+0.5\cdot200\cdot150\cdot\sin\frac{\pi}{3}\cdot\frac{\pi}{90}$
$dA=458.8...m^2$