Question

Find the tangent of the angle in between the lines 2x+3y–5=0 and 5x=7y+3?

Answer 1

tanФ = 2.6363636

Explanation:

To find the tangent of the angle in-between the lines we will follow the steps below:

We are going to use the formula;

tanФ = |m₂ - m₁ / 1 + m₁m₂|

We can get the slope m₁ from the first equation

2x+3y–5=0

we will re-arrange it in the form y=mx + c

3y = -2x + 5

Divide through by 3

y = -
`(2)/(3)`x +
`(5)/(3)`

comparing the above equation with y=mx + c

m₁ = -
`(2)/(3)`

We will proceed to find the second slope m₂ using the second equation

5x=7y+3

we will re-arrange it in the form y=mx + c

7y = 5x -3

divide through by 7

y =
`(5)/(7)` x -
`(3)/(7)`

comparing the above with y=mx + x

m₂ =
`(5)/(7)`

we can now go ahead and substitute into the formula

tanФ = |m₂ - m₁ / 1 + m₁m₂|

tanФ = |
`(5)/(7)` - (-
`(2)/(3)` ) / 1 + (-
`(2)/(3)`₁)(
`(5)/(7)`)|

tanФ = |
`(5)/(7)` +
`(2)/(3)` / 1 -
`(10)/(21)`|

tanФ = |
`(29)/(21)` /
`(11)/(21)`|

tanФ = |
`(29)/(21)` ×
`(21)/(11)`|

21 will cancel-out 21

tanФ =
`(29)/(11)`

tanФ = 2.636363