Question

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

Answer 1

Answer:

tanФ = 2.6363636

Step-by-step 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 = -$\frac{2}{3}$x + $\frac{5}{3}$

comparing the above equation with y=mx + c

m₁ =  -$\frac{2}{3}$

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 = $\frac{5}{7}$ x -  $\frac{3}{7}$

comparing the above with y=mx + x

m₂ = $\frac{5}{7}$

we can now go ahead and substitute into the formula

tanФ = |m₂ - m₁  / 1 + m₁m₂|

tanФ = | $\frac{5}{7}$ -  (-$\frac{2}{3}$ ) / 1 +  (-$\frac{2}{3}$₁)( $\frac{5}{7}$)|

tanФ = | $\frac{5}{7}$ +$\frac{2}{3}$  / 1 -  $\frac{10}{21}$|

tanФ = | $\frac{29}{21}$ / $\frac{11}{21}$|

tanФ = | $\frac{29}{21}$ × $\frac{21}{11}$|

21 will cancel-out 21

tanФ =$\frac{29}{11}$

tanФ = 2.636363