Question

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB, and sin _X = 5.59

Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ABC. You must show all work and calculations to receive full credit. (5 points)
Part B: Explain how to find the measures of segments CB and AB. You must show all work and calculations to receive full credit. (5 points)

Answer 1

When triangle XYZ is dilated to create triangle ABC, the trigonometric ratios of the angles remain the same. The measures of segments CB and AB can be found using the property of corresponding sides in similar triangles.

Step-by-step explanation:

When triangle XYZ is dilated by a scale factor of 2 to create triangle ABC, the trigonometric ratios of the angles in the two triangles remain the same. This means that the sine, cosine, and tangent ratios in triangle ABC will be the same as those in triangle XYZ. For example, if sin X is 5.59 in triangle XYZ, sin A will also be 5.59 in triangle ABC.

To find the measures of segments CB and AB, we can use the property that the lengths of corresponding sides of similar triangles are proportional. Since triangle ABC is a dilation of triangle XYZ with a scale factor of 2, the lengths of corresponding sides in the two triangles are related by the equation AB = 2XY and CB = 2XZ.