Question

Find the cosine of the angle $A$ of the triangle with vertices $A(1,-1),B(6,11)$ and $C(1,2)$.

Answer 1

Slope of side $AB$ is $\frac{11+1}{6-1}=2.4$

Angle made with $X-axis$ is ${\tan }^{-1}2.4$

Since $AC$ is parallel to $Yaxis$ angle made with Y-axis is $\frac{\pi }{2}-{\tan }^{-1}2.4={\text{cot}}^{-1}\left(2.4\right)={\text{cot}}^{-1}(\frac{12}{13})$

$⟹\cot A=\frac{12}{13}$