Find the area given the following description: From an iron post, proceed 500 m northeast to the brook, then 300 m east along the brook to the old mill, then 200 m S 15° E to a post on the edge of Wiggin's Road and finally along Wiggin's Road back to the iron post.
For this problem, I was told to assume that whenever the word northeast, southwest, or some other combination of cardinal directions was used, then the bearing would be 45°.
I tried drawing this picture, but I can't figure out the angles I need to find the areas of the triangles (I was thinking of dividing the figure into 2 triangles and then using either of the formulas $\sqrt{(s(s-a)(s-b)(s-c)}$, $\frac{bh}{2}$, or $\frac{1}{2}bc \sin C$ where C is the angle between sides $b$ and $c$.
Any help on how to draw the problem and solve for the angles would be appreciated.
Thanks.
Best Answer
Oops. I forgot to put the distance in the picture. post to brook is $500$, $m\angle Post-brook-mill = 135$ (going from NE to due E). Brook to old mill is $300$. $m\angle brook-mill-wiggins=105$ (going from due east to south ($90$ and eat by $15$ degrees). And old mill to wiggins rd is $200$.
So .... have at it.