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Triangles 1 and 2 are similar. What ratio relates a side length of triangle 1 to the corresponding side length of triangle 2? Fill in the box to complete the ratio.

Triangle ABC (Triangle 1):
- Side AC = 17
- Side CB = 15
- Side AB = 8
- Angle C = 28 degrees
- Angle A = 62 degrees

Triangle DEF (Triangle 2):
- Side DF = 25.5
- Side FE = 22.5
- Side DE = 12
- Angle D = 62 degrees
- Angle F = 28 degrees
- Angle E = 90 degrees

Answer :

If triangles 1 and 2 are similar, the ratio relates a side length of triangle 1 to the corresponding side length of triangle 2 is 2:3.

Since Triangles 1 and 2 are similar, their corresponding sides are proportional. This means that the ratio of the length of any corresponding pair of sides in the two triangles will be equal.

To determine the ratio of the side lengths of triangle 1 to the corresponding side lengths of triangle 2, we can choose any two corresponding sides and divide their lengths.

Let's choose side AC of triangle 1 and side DF of triangle 2. We know that these two sides are corresponding because they are both opposite angles that have the same measure.

The length of side AC in triangle 1 is given as 17, and the length of side DF in triangle 2 is given as 25.5. Therefore, the ratio of the length of side AC to side DF is:

AC/DF = 17/25.5 = 0.6667 or 2/3

So the ratio of the length of a side in triangle 1 to the corresponding side in triangle 2 is 2:3. This means that if we multiply any side length in triangle 1 by 2, we will get the length of the corresponding side in triangle 2.

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