I am trying to help my daughter with a problem from Stewart's Precalculus book.This problem comes right after law of sines.
When two bubbles cling together in midair, their common surface is part of a sphere whose center D lies on the line passing through the centers of the bubbles (please refer to the figure below) also angles ACB and ACD each have measure 60 degrees
- Show that the radius r of the common surface is given by r = ab / (b - a)
- Find the radius of the common face if the radii of the bubbles are 3cm and 4cm
I could do the second one but after using law of cosines to find length of the segment AB in triangle CBA. That came out as Then I used law of sines in triangle ABC to find angle CAB = 73.897 degrees
Angle CAD = 180 - angle CAB = 106.1 degrees angle CDA = 180 - 106.1 - 60 = 13.897 degrees
Then I used law of sines in triangle CAD to find the value of r
But I couldn't make any headway for the first one. Also it seems to me that I don't need law of cosines to solve this problem.