We know the angle, the side opposite to the angle(91), and we want to find the side adjacent to the angle(x). Which property is the ratio of the opposite and adjacent sides?
[tex]\sf sin(x\textdegree )=\dfrac{Opposite}{Hypotenuse}[/tex]
[tex]\sf cos(x\textdegree )=\dfrac{Adjacent}{Hypotenuse}[/tex]
[tex]\boxed{\sf tan(x\textdegree )=\dfrac{Opposite}{Adjacent}}[/tex]
Let's use tangent:
[tex]\sf tan(55\textdegree )=\dfrac{91}{x}[/tex]
Solve for 'x', multiply 'x' to both sides:
[tex]\sf tan(55\textdegree )x=91[/tex]
Divide the tangent of 55 degrees to both sides:
[tex]\sf x=\dfrac{91}{tan(55\textdegree )}[/tex]
This is an exact answer, if you want an approximate:
[tex]\sf x\approx 63.72[/tex]
