# Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = .Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ACB.

Part A:
When a triangle is dilated by a scale factor of 2, the trigonometric ratios for each angle and side are doubled. This means that if we know the sin ∠X in triangle XYZ, then we can calculate the sin ∠A in triangle ACB using the following equation:

sin ∠A = (scale factor)(sin∠X) = (2)(sin∠X)
In this case, because the scale factor is 2 and sin ∠X = .
We can conclude that sin ∠A = 2(. )= .

## Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = .Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ACB.

Part B: To find the measures of segments CB and AB in triangle ACB, we must use our knowledge of similar triangles. Since Triangle XYZ was dilated to create Triangle ACB, we know these two triangles are similar by definition. As such, their sides will be proportional based on their corresponding angles. The ratio between corresponding sides can be found using either sine or cosine ratios depending on whether our known angle is an acute or obtuse angle respectively. In this case our known angle is an acute one – thus, I would suggest finding both CB and AB via sine ratios as follows:
CB/XY = Sin(∡C)/Sin(∡X)= Sin(2∡X)/ Sin(∡X)=2 —> Cb= 2*XY        and         AB/YZ= Sin(∡A)/Sin(ˆY)=Sin (2ˆx)/Sinˆy=2      —>    AB= 2*YZ

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