## Angle Between Lines Drawn Through Rectangle

Given a rectangle with two straight lines drawn through, we can find the angle between the lines. If the gradients of the lines are\[m_1\]

and \[m_2\]

with \[m_1 \gt m_2\]

then the angle between the lines is \[tan^{-1} (m_1) - tan^{-1}(m_2)\]

.The line

\[l_1\]

goes along 7+3=10 and up 6-3=3. The gradient is \[\frac{3}{10}\]

.The line

\[l_2\]

goes along 3-6=-3 and up 3+5=8. The gradient is \[\frac{8}{-3}\]

.The angle

\[\alpha\]

is \[tan^{-1}( \frac{8}{-})- tan^{-1}(\frac{3}{10})=93.9^o\]

to 1 decimal place.