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 1804 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.htmlHope it helps.

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