# Angle's rate decreasing

1. Jul 12, 2013

1. The problem statement, all variables and given/known data
Look at the image.All the O's are of equal length.O1=O2=O3 etc.Angles are subtended from two ends of An O to point P.As you see,O1's angle is larger than O2 ant )2's angle is larger then O3 and so on.
As you Go down the O's(i.e. O1,O2,O3 etc),the angle subtented by the O's Decrease and that too with a decreasing rate.
What would be the angle of nth O.

2. Relevant equations
a+d(n-1)
ar^(n-1)

3. The attempt at a solution
As the angles decrease with decreased rate,The Formulas are not usable.
What should I do?Angles are not even inversely proportional to O's.

#### Attached Files:

• ###### Angles.png
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2. Jul 12, 2013

### szynkasz

You can use the cosine rule. Lengths of two "rays" can be calculated from Pythagorean theorem.

3. Jul 12, 2013

What could be the angle of nth O?
And I haven't studied Cosine rule yet.I am In Gr 9.

4. Jul 12, 2013

### szynkasz

Rays are hypotenuses of right angles so you can use tangent function instead. The angle of nth O is a difference of angles of nth and n-1th triangle.

5. Jul 12, 2013

I don't Understand

6. Jul 12, 2013

### szynkasz

Let $PO$ be the segment from $P$ to the line of $O$'s Together with $a$ and $O_1$ it makes a right triangle so you can calculate $\tan\alpha_{\small O_1}$

7. Jul 12, 2013

### Strants

Just to make sure everyone's on the same page: adjacent, do you know trigonometric functions (Sine, Cosine, Tangent)?

8. Jul 13, 2013

Yes.But
Only sineθ=Opposite/Hypotenuse
But that's for Right angle triangle only.Right?

Assume that we don't know any thing about the length of the lines.Only Length of O and Angles(on the side of P) are given.We are to calculate,for example,For O1,the angle is this much.For O2 The angle would be that much.Then For On what would be the angle?

Last edited: Jul 13, 2013
9. Jul 13, 2013

### szynkasz

$PO,2O,b$ also makes right triangle. So the angle for 2nd $O$ is $\alpha_{\small O_2}-\alpha_{\small O_1}$