The portion of the line 4 x+5 y=20 in the first quadrant is trisected by the lines L_1 and…

Question

The portion of the line $4 x+5 y=20$ in the first quadrant is trisected by the lines $\mathrm{L}_1$ and $\mathrm{L}_2$ passing through the origin. The tangent of an angle between the lines $\mathrm{L}_1$ and $\mathrm{L}_2$ is :

Accepted Answer

Co-ordinates of $$\mathrm{A}=\left(\frac{5}{3}, \frac{8}{3}\right)$$

Co-ordinates of $$\mathrm{B}=\left(\frac{10}{3}, \frac{4}{3}\right)$$

Slope of $$\mathrm{OA}=\mathrm{m}_1=\frac{8}{5}$$

Slope of $$\mathrm{OB}=\mathrm{m}_2=\frac{2}{5}$$

$$\begin{aligned}
& \tan \theta=\left|\frac{m_1-m_2}{1+m_1 m_2}\right| \
& \tan \theta=\frac{\frac{6}{5}}{1+\frac{16}{25}}=\frac{30}{41} \
& \tan \theta=\frac{30}{41}
\end{aligned}$$

Solutions · 1