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# Ratio between angles and sides in a right angle traingle.

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Ratio between angles and sides in a right angle traingle. [#permalink]

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02 May 2012, 09:32
Is there a general formula or an idea to calculate the ratio between the angles when sides are given and/or vice-versa?
Can this be applied to non-right angle triangles too?
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Re: Ratio between angles and sides in a right angle traingle. [#permalink]

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02 May 2012, 09:41
I don't think there's any relation between side length and angle. I just add or subtract the angles.
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Re: Ratio between angles and sides in a right angle traingle. [#permalink]

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02 May 2012, 09:56
Expert's post
Moving to the Quant forum.
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Manager
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Re: Ratio between angles and sides in a right angle traingle. [#permalink]

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02 May 2012, 10:23
@Jay: There is ,in the case of a right angle triangle.
One has to do some manipulations over the base, perpendicular and hypotenuse of the angles.
I have very little memory of what has to be done exactly.
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02 May 2012, 21:00
In a general case, there is no relation between angles and sides of a triangle.
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04 May 2012, 21:07
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A,B,C being three sides in a triangle.

Ratio between them is a:b:c.
Let c be the hypotenuse.

Divide the above ration with c.
So the ratio between the sides is a:b:c is equivalent to a/c:b/c:c/c.

we know that a/c, b/c ,c/c is the sin,cos and tan of one the angle.
So you will get the ratio accordingly.
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Re: Ratio between angles and sides in a right angle traingle. [#permalink]

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17 May 2012, 01:22
There is NO relation between Angles and Sides of a triangle.
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Re: Ratio between angles and sides in a right angle traingle. [#permalink]

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21 May 2012, 15:26
No relation.

A 30-60-90 triangle with sides of 3-4-5 has ratios of 1:2:3 (angles) and 3:4:5 (sides). It could also have the same angle ratios but have side ratios as 5:12:13.
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25 May 2012, 19:00
in case of a 30-60-90 triangle the sides opposite the respective angles have the following relative lengths x sq rt 3) x : 2x

In case of a 45:45:90 triangle the sides are in the following proportion x:x:(sq rt 2) x

Generally the side opposite the largest anlge is the biggest side and the side opposite the smallest angle is the smallest side.
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Re: Ratio between angles and sides in a right angle traingle. [#permalink]

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27 May 2012, 06:24
Hi,

Here is the general formula (applicable to any triangle),
$$a/sinA = b/sinB = c/sinC$$ (out of scope of GMAT)

And as per GMAT,
for a right angles triangle only two combinations of angles are useful, i.e, 30,60,90 where ratio of sides is 1:\sqrt{3}:2
and 45,45,90 -> ratio of sides - 1:1:\sqrt{2}

Regards,

Last edited by cyberjadugar on 27 May 2012, 09:39, edited 1 time in total.
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27 May 2012, 08:26
cyberjadugar I dont think trigonometry is under gmat syllabus.
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Re: Ratio between angles and sides in a right angle traingle. [#permalink]

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27 May 2012, 09:38
vibhav wrote:
cyberjadugar I dont think trigonometry is under gmat syllabus.

Agreed, trigonometry is not covered in GMAT.

Mentioned the formula just for the sack of learning, if anyone is interested.
Re: Ratio between angles and sides in a right angle traingle.   [#permalink] 27 May 2012, 09:38
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