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# If the measures of the angle in a triangle are in the ratio

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Intern
Joined: 29 Sep 2011
Posts: 16
If the measures of the angle in a triangle are in the ratio [#permalink]

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19 Jan 2012, 16:25
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45% (medium)

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57% (00:44) correct 43% (00:32) wrong based on 171 sessions

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If the measures of the angle in a triangle are in the ratio of 1:2:3, what is the ratio of the smallest side of the triangle to the largest side?

A. 1:2
B. 1:3
C. 1:5
D. 2:3
E. 2:5
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 43898

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19 Jan 2012, 17:08
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Splendidgirl666 wrote:
Hi,
can someone help with this one please?

If the measures of the angle in a triangle are in the ratio of 1:2:3, what is the ratio of the smallest side of the triangle to the largest side?

1. 1:2
2. 1:3
3. 1:5
4. 2:3
5. 2:5

The measures of the angle in a triangle are in the ratio of 1:2:3 --> $$x+2x+3x=180$$ --> $$6x=180$$ --> $$x=30$$, $$2x=60$$ and $$3x=90$$. We have a right triangle where the angles are 30°, 60°, and 90°.
Attachment:

Math_Tri_Right3060.png [ 3.64 KiB | Viewed 10310 times ]

This is one of the 'standard' triangles you should be able recognize on sight. A fact you should commit to memory is: The sides are always in the ratio $$1:\sqrt{3}:2$$.

Notice that the smallest side (1) is opposite the smallest angle (30°), and the longest side (2) is opposite the largest angle (90°).

So the ratio of the smallest side of the triangle to the largest side is 1/2.

Check Triangles chapter of Math Book for more on this topic: math-triangles-87197.html

Hope it helps.
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Joined: 25 Oct 2013
Posts: 165
Re: If the measures of the angle in a triangle are in the ratio [#permalink]

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07 Mar 2014, 02:14
If angles are in ratio of 1:2:3 the triangle becomes a 30-60-90 triangle. ratio of sides is 1:$$\sqrt{3}$$:2 hence answer is 1:2.
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Intern
Joined: 28 Nov 2017
Posts: 1
Re: If the measures of the angle in a triangle are in the ratio [#permalink]

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07 Feb 2018, 10:37
could you please explain how you get the side lengths from the ratio 1:2:3.From the ratio we get 30-60-90 right triangle. which has the side lengths like X-X\/3-2x.now how you found 1,2,\/3?
Re: If the measures of the angle in a triangle are in the ratio   [#permalink] 07 Feb 2018, 10:37
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