Given 2 coordinates and an angle of a triangle, what is the third coordinate?

Question

I know I can calculate the distance between B and D using the law of cosines, but I am lost when finding the coordinates for D.

What is the best way?

Answer 1

Assume the point $(x,y)$

Use these $2$ equations..

$$(x-7.84)^2+(y-39.2)^2=2.57^2$$

And

$\cos 16.3={2.57^2+40^2-(x^2+y^2)\over 2\times 2.57\times 40}$