Question

Given the triangle and equation below, what is the value of x?



sec∠C - cot∠A = 3x

Answer 1

Without knowing the lengths of the sides of the triangle, this is difficult.
However, a general case can be made.


Using these lengths specified,

sec(C)-cot(A)=3x turns into:

\[\sqrt{A^2+C^2}/C-A/C=3X\]
\[\rightarrow \sqrt{A^2+C^2}-A=3X\]
\[\rightarrow C^2=9X^2C^2+3AXC\]
\[\rightarrow (9C)X^2+(3A)X-C=0\]
Using the quadratic equaiton:
\[\rightarrow X=(-A \pm \sqrt{A^2+4C^2})/(6C)\]