The portion of the line $4x+5y=20$ in the first quadrant is trisected by the lines $L_1$ and $L_2$ passing through the origin. The tangent of an angle between the lines $L_1$ and $L_2$ is:
Step-by-Step Solution
Key Concept: The line $4x+5y=20$ has intercepts $(5,0)$ and $(0,4)$. Trisection points: $A=(5/3,8/3)$ and $B=(10/3,4/3)$. Slopes: $m_1=8/5$ (line $L_1$ through $A$) and $m_2=2/5$ (line $L_2$ through $B$). Angle between them via $\tan\theta=|m_1-m_2|/(1+m_1m_2)$.
$\tan\theta=\frac{30}{41}$.
Correct Answer: 4