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605-655 (Medium)|   Geometry|      
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Splendidgirl666
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If the measures of the angle in a triangle are in the ratio 19 Jan 2012, 17:25
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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
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A
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Bunuel
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If the measures of the angle in a triangle are in the ratio 19 Jan 2012, 18:08
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Splendidgirl666
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
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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
Math_Tri_Right3060.png [ 3.64 KiB | Viewed 56127 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.

Answer: A.

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

Hope it helps.
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If the measures of the angle in a triangle are in the ratio 07 Mar 2014, 03:14
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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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If the measures of the angle in a triangle are in the ratio 07 Feb 2018, 11:37
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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?
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If the measures of the angle in a triangle are in the ratio 17 Apr 2019, 18:50
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Splendidgirl666
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
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We can determine the 3 angles:

x + 2x + 3x = 180

6x = 180

x = 30

So the angles are 30, 60, 90, thus the ratio of sides are:

x : x√3 : 2x

So the ratio of smallest : largest = x : 2x = 1 : 2

Answer: A
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If the measures of the angle in a triangle are in the ratio 20 Apr 2019, 13:41
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sakeba
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?
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Do you understand it now or do you still need an explanation?
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If the measures of the angle in a triangle are in the ratio 07 Sep 2020, 12:47
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