SOLUTION: Could you please help me with this problem? It's using perfect triangles and the sine rule - I can get it up to a point and have put it into wolfram alpha to get the solution, but

Algebra ->  Trigonometry-basics -> SOLUTION: Could you please help me with this problem? It's using perfect triangles and the sine rule - I can get it up to a point and have put it into wolfram alpha to get the solution, but       Log On


   

Question 845703: Could you please help me with this problem? It's using perfect triangles and the sine rule - I can get it up to a point and have put it into wolfram alpha to get the solution, but I have no idea how to work it out properly: { { { (4x+10)/(sin(30°)) = (6x+2)/(sin(45°)) } } } for x
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi

%284x%2B10%29%2Fsin%2830%29+=+%286x%2B2%29%2Fsin%2845%29

%282x%2B5%29%2Fsin%2830%29+=+%283x%2B1%29%2Fsin%2845%29

%282x%2B5%29%2F%281%2F2%29+=+%283x%2B1%29%2F%28sqrt%282%29%2F2%29

%282x%2B5%29+=+%283x%2B1%29%2Fsqrt%282%29

2sqrt%282%29x%2B5sqrt%282%29+=+%283x%2B1%29+%29

3x+-+2sqrt%282%29x+=+5sqrt%282%29+-+1

x%283+-+2sqrt%282%29%29+=+5sqrt%282%29+-+1

x=+%285%2Asqrt%282%29+-+1%29%2F%283-2sqrt%282%29%29  |multiplying N & D by conjugate %283%2B2sqrt%282%29%29

 x+=++%2815sqrt%282%29-3%2B20-2sqrt%282%29%29%2F%289-8%29+=+17+%2B+13sqrt%282%29