Jessica A.

asked • 03/09/22

Geometry Study guide

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and sin ∠X = 5 over 5 and 59 hundredths.

Triangles XYZ and ACB; angles Y and C both measure 90 degrees, angles A and X are congruent.


Part A: Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ACB. 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.


Jessica A.

Please explain what you did!! Sometimes it is a little confusing!
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03/09/22

Brenda D.

tutor
A. You have a right triangle. In a right triangle the side opposite the 90 degree angle is the longest side or Hypotenuse for the other angles such as angle X the sine is the length of the side opposite angle X/the length of the hypotenuse. According to the ratio given for Triangle XYZ the side opposite angle X is 5 and the Hypotenuse is 5.59. B. You doubled the length of each side of triangle XYZ to create Triangle ABC but there is no change in the size of the angles so the sine of A is the same as the sine of X. You can review the Trigonometric ratios associated with Right Triangles and the relationships between Similar Triangles online or in your text.
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03/09/22

1 Expert Answer

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Donald W. answered • 03/09/22

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A. Here are a couple of the trigonometric ratios: sin ∠X = YZ/XZ. cos ∠A = AC/AB. Can you figure out the other ratios? Use the mnemonic SOHCAHTOA to help you.


B. Based on A and the information given in the problem, we know that YZ = 5 and XZ = 5.59. Can you use that along with additional information given to you to figure out the lengths of CB and AB?

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