Question

How do you find a if given c and 0 (angle) in a right triangle where a is the opposite, c is the hypotenuse, b is adjacent and 0 is the angle in between c and b?

Answer 1

c can be found using pythagoras theorem. c2=a2+b2. Now, b is not given, but we know that cos(theta)=b/c=>b=c*cos(theta). Substituting b in the above relation, c2=a2+c2(cos(theta))^2=>c2=a2/(1-cos((theta))^2). c is the squareroot of c2. Hence c=sqrt(2/(1-cos((theta))^2))