Question

X=? Y=6
75 degree angle at (0,0)
What is X?

Answer 1

`X=12-6√(3)=1.6077`

Explanation:

Given that
`Y=6`

`\tan(75)=(Y)/(X) \\X=(Y)/(\tan(75))=Y\cot75=6\cot75 \\\\Calculate \ \cot(75)\\\tan(75)=\tan(45+30)=(\tan45+\tan30)/(1-\tan45 \cdot \tan30) =(1+(1)/(√(3) ) )/(1-(1)/(√(3) ) ) \\\tan75=(√(3)+1 )/(√(3)-1 ) =2+√(3) \\\cot75=(1)/(2+√(3) ) =(2-√(3) )/(2^2-3) =2-√(3) \\\\Hence\\X=6\cot75=6 \cdot(2-√(3))\\X=12-6√(3) \approx1.6077`