Find point with two angles

**desiderius1** · January 30th 2011, 12:37 PM

Hello,

I am trying to a find a point on a x,y plane from two angles.

Let's say the X,Y plane is 1000 by 1000 and the point I am looking for is (700,300).

Angle from (0,0) to point is 23.2*
Angle from (1000,0) to point is -45*

I already gave the answer, I'm just curious how to find a point with two angles on a grid.

Here is a visual representative of the problem.

**pickslides** · January 30th 2011, 12:58 PM

Originally Posted by desiderius1

the point I am looking for is (700,300).

Do you really mean (700, -300) ?

**desiderius1** · January 30th 2011, 01:12 PM

Hmm.. I don't know if I'm calculating the angles right. Sorry I have never taken trig before.

From point (700,300) to (0,0)
atan2((700-0),(300-0)) = 23.2*

and point (700,300) to (1000,0)
atan2((700-1000),(300-0)) = 135*

Is this correct, if so, how would I find the intersection point of these two angles?

**desiderius1** · January 30th 2011, 04:37 PM

Anyone?

**earboth** · January 30th 2011, 11:22 PM

Originally Posted by desiderius1

Hello,

I am trying to a find a point on a x,y plane from two angles.

Let's say the X,Y plane is 1000 by 1000 and the point I am looking for is (700,300).

Angle from (0,0) to point is 23.2*
Angle from (1000,0) to point is -45*

I already gave the answer, I'm just curious how to find a point with two angles on a grid.

1. I've modified your sketch a little bit. (see attachment)

2. Calculate the 3rd angle: $|\alpha| = 111.8^\circ$

3. Use the sine rule to calculate the length of x:

$\dfrac x{1000}=\dfrac{\sin(45^\circ)}{\sin(111.8^\circ)}~ \implies~x \approx 761.57$

4. The point P has the coordinates $P\left(x\cos(23.2^\circ)\ , \ x\sin(23.2^\circ) \right)$

**desiderius1** · February 11th 2011, 02:34 AM

I have another scenario of this. How would I find the point listed (?,?) in the picture that I drew?

From point (0,0) to point (600,575), the angle is 43.7805 degrees.
From point (?,?) to point (600,575), the angle is 65.2698

I then subtracted both these angles to get the angle in-between the two lines, which if I am correct, is 21.4893 degrees.

So now, what do I do from here?

Thank you.

ANSWER: The point (?,?) is 512,384. I just want to know how to get it.

**HallsofIvy** · February 11th 2011, 03:36 AM

If all you know is a single angle (the angle of the line from (0,0) to (600,575) is irrelevant to this problem), there is no way to find the point. Any point on that line your picture shows from (600,575) to (?, ?) satisfies the conditions.

**desiderius1** · February 11th 2011, 03:41 AM

Is it possible to find out the point (?,?) if you knew the angle from (0,0) to (?,?), which happens to be, in this case, 36.87*. Thank you for replying.

**earboth** · February 11th 2011, 05:15 AM

Originally Posted by desiderius1

Is it possible to find out the point (?,?) if you knew the angle from (0,0) to (?,?), which happens to be, in this case, 36.87*. Thank you for replying.

First of all: Do yourself and do us a favour and start a new thread if you have a new question. Otherwise you risk that nobody will notice your need for help.

1. Calculate the length $|\overline{PQ}|\approx 831$

2. Calculate all interior angles of the triangle OPQ:
$\angle(POQ) = 6.9105^\circ$
$\angle(QPO) = 21.4895^\circ$
$\angle(PQO) = 151.6^\circ$

3. Use the Sine rule to calculate the length of x:

$\dfrac x{831}=\dfrac{\sin(21.4893)}{\sin(151.6)}~\implies ~x \approx 640$

4. The coordinates of Q are $Q\left(x \cdot \cos(36.87^\circ)\ ,\ x \cdot \sin(36.87^\circ) \right)$

**desiderius1** · February 11th 2011, 05:29 AM

Thank you very much. Also I will start a new thread next time, sorry for that.

**desiderius1** · February 13th 2011, 09:13 AM

I debated starting a new thread for this but figured it wouldn't make much sense, since it is a continuation of the problem stated above.

Anyways, How do I find the point P, pretending that was the unknown point. I tried changing the formula around by couldn't get my answer to be (600,575)

**earboth** · February 13th 2011, 11:23 PM

Originally Posted by desiderius1

I debated starting a new thread for this but figured it wouldn't make much sense, since it is a continuation of the problem stated above.

Anyways, How do I find the point P, pretending that was the unknown point. I tried changing the formula around by couldn't get my answer to be (600,575)

1. To locate a point in the plane we need to know one distance and two angles OR two distances and one angle.

2. You have to tell us which parts of the situation are known. And then we can show you how to get the coordinates of point P.

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