Question

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

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

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)

Can someone explain this to me?

Answer 1

The trigonometric ratios of both the Triangle are equal and AC = 2 * XY; CB = 2 * YZ

What is Dilation ?

Dilation is when a given figure is stretched or compressed by a factor , known as scale factor keeping its shape intact.

Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB,

Therefore it can be said that

XYZ is similar to ACB

Angle Y = 90 degrees

Angle  C= 90 degrees,

angles A and X are congruent.

Given is sin∠X = 5/5.59

Ton calculate the base of the triangle when perpendicular to angle X is 5 and hypotenuse is 5.59

By Pythagoras Theorem

XY = √((5.59)² - 5²) ≅ 2.5

So,

tanX = tanA = 5/2.5

CB/YZ = 2 ( given)

Therefore

AC = 2 * XY

To know more about Dilation

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