Find Slope of 1st Line w/ Given Data

[markram987]

finding the slope??

how to find the slope of 1st line?. when 2nd line slope is given, angle between them is given, the intersection of the 2 lines are given also... any ideas?
see this
http://img87.imageshack.us/img87/1055/questionz.png

 

[chiro]

how to find the slope of 1st line?. when 2nd line slope is given, angle between them is given, the intersection of the 2 lines are given also... any ideas?
see this
http://img87.imageshack.us/img87/1055/questionz.png

Do you know the relationship between the slope of a line and its tangent?

 

[markram987]

Do you know the relationship between the slope of a line and its tangent?

you mean tangent theta= slope?? so what's the specific formulai can use?

 

[chiro]

Yes that's the formula.

So given that tan(theta) = m2 and given we know what m2 is, do you know how to get theta by itself? Do you know about inverse functions?

(Hint tan^-1(tan(theta)) = theta if 0 <= theta < pi))

 

[markram987]

(Hint tan^-1(tan(theta)) = theta if 0 <= theta < pi))

i didn't understand your hint.
the theta or angle are given and i know the high school inverse function..
i will thank you if you just let type the formula here or equate it to m1 and then i will think how it is derive.. if i didn't know i will ask you question^^

 

[chiro]

i didn't understand your hint.
the theta or angle are given and i know the high school inverse function..
i will thank you if you just let type the formula here or equate it to m1 and then i will think how it is derive.. if i didn't know i will ask you question^^

Ok then I will give you the answer and go through it step by step.

As you may know the tangent is calculated using rise over a run. So basically if our tangent was +1 it means that if my x moves one unit to the right, then my y moves one unit up. If it was +2 it means if i move one unit to the right, then my y moves two units up.

If it was say -1, it means that if i move my x one unit to the right then my y goes down one.

Now going back to trigonometry of right angled triangles we know that tan = opposite over adjacent which is what the tangent is: remember its a line and if we form a triangle with our x and y we get a right angled triangle.

So you know that m2 = (y2 - y1)/(x2 - x1) = tan(theta).

So to find theta if we have m2, we use the formula:

theta = tan^-1(m2). If you haven't seen tan^-1 it means the "inverse tangent" and it is also called "arctan". If you have a calculator it will probably say "tan^-1).

So let's say your m2 was 1 for example.

theta = tan^-1(1) = 45 degrees.

Now you have gotten the angle for the line, you add the angle that you're given in your question and to get the slope of the line we are trying to find you calculate it using

Lets pretend the angle you are given is 90 degrees.

Your answer for finding slope for line 2 would be found by calculating:

m1 = tan(45 + 90) = tan(135) = -1.

Also if you're using a calculator make sure its set to degrees if you're working in degrees.

 

[zgozvrm]

you mean tangent theta= slope?? so what's the specific formulai can use?

... so, since you know the slope of line2, you can determine the angle it makes with the positive x-axis, right? Call that angle [itex]\alpha[/tex]

Once you find that, simply add the angle [itex]\Theta[/tex] (the angle between the lines) to that [itex](\beta = \Theta + \alpha)[/tex] and find the slope of the line that makes an angle of [itex]\beta[/tex] with the positive x-axis.

 

[markram987]

Ok then I will give you the answer and go through it step by step.

As you may know the tangent is calculated using rise over a run. So basically if our tangent was +1 it means that if my x moves one unit to the right, then my y moves one unit up. If it was +2 it means if i move one unit to the right, then my y moves two units up.

If it was say -1, it means that if i move my x one unit to the right then my y goes down one.

Now going back to trigonometry of right angled triangles we know that tan = opposite over adjacent which is what the tangent is: remember its a line and if we form a triangle with our x and y we get a right angled triangle.

So you know that m2 = (y2 - y1)/(x2 - x1) = tan(theta).

So to find theta if we have m2, we use the formula:

theta = tan^-1(m2). If you haven't seen tan^-1 it means the "inverse tangent" and it is also called "arctan". If you have a calculator it will probably say "tan^-1).

So let's say your m2 was 1 for example.

theta = tan^-1(1) = 45 degrees.

Now you have gotten the angle for the line, you add the angle that you're given in your question and to get the slope of the line we are trying to find you calculate it using

Lets pretend the angle you are given is 90 degrees.

Your answer for finding slope for line 2 would be found by calculating:

m1 = tan(45 + 90) = tan(135) = -1.

Also if you're using a calculator make sure its set to degrees if you're working in degrees.

thank you^^ you have nice tutorial...
did you mean that this is the right formula? m1 = tan((tan^-1(m2))+given angle) or m1 = tan(theta + given angle)

it is also the same with this formula tan(theta1-theta2)= ((m2-m1)/(1+(m1*m2)))?

 

[markram987]

... so, since you know the slope of line2, you can determine the angle it makes with the positive x-axis, right? Call that angle [itex]\alpha[/tex]

Once you find that, simply add the angle [itex]\Theta[/tex] (the angle between the lines) to that [itex](\beta = \Theta + \alpha)[/tex] and find the slope of the line that makes an angle of [itex]\beta[/tex] with the positive x-axis.

can you give example?

 

[zgozvrm]

can you give example?

We are given slope m2 and angle [itex]\Theta[/tex] between the two lines.


Let's say we have m2 = 0.404 and [itex]\Theta = 75^\circ[/tex].

Then we know that Line 2 makes an angle of [itex]\alpha = \tan ^{-1}(0.404) = 22^\circ[/tex] with the positive x-axis.
The angle that line 1 makes with the positive x-axis is [itex]\beta = \alpha + \Theta = 22 + 75 = 97^\circ[/tex]

The slope of line 1 would then be [itex]\tan (\beta) = \tan(97^\circ) = -8.144[/tex]

 

[markram987]

We are given slope m2 and angle [itex]\Theta[/tex] between the two lines.Let's say we have m2 = 0.404 and [itex]\Theta = 75^\circ[/tex].

Then we know that Line 2 makes an angle of [itex]\alpha = \tan ^{-1}(0.404) = 22^\circ[/tex] with the positive x-axis.
The angle that line 1 makes with the positive x-axis is [itex]\beta = \alpha + \Theta = 22 + 75 = 97^\circ[/tex]

The slope of line 1 would then be [itex]\tan (\beta) = \tan(97^\circ) = -8.144[/tex]

nice ,it is the same but a simple standard equation..
can u post a picture with that 22degree and 97degree because i can't imagine the angle positon..
..

 

[zgozvrm]

nice ,it is the same but a simple standard equation..
can u post a picture with that 22degree and 97degree because i can't imagine the angle positon..
..

Sure! Here you are...