kmarcus602
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Please answer quick!
Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and tan ∠X = 5 over 2 and 5 tenths.




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 AC and CB. You must show all work and calculations to receive full credit. (5 points)

Please answer quick Triangle XYZ was dilated by a scale factor of 2 to create triangle ACB and tan X 5 over 2 and 5 tenths Triangles XYZ and ACB angles Y and C class=

Respuesta :

s696808

Answer:

Let's first find the side lengths for triangle XYZ

assuming you know that tan is opposite over adjacent, we know that

YZ = 5

XY=2.5

And because triangle XYZ was dilated with a scale factor of 2, to create the other triangle, we know for sure that these two triangles are similar, and the angles are equal too

angle C equals angle Y

angle A equals angle X

angle B equals angle Z

And the special relationship is, that they are all equal, because with a scale factor of two, all the trig ratios in triangle ABC will simplify to the trig ratios of triangle XYZ

Not sure when it says "You must show all work and calculations to receive full credit." does it want you to write all the trig ratios out-?

You could write the tan values of each angle, adn compare them with the other triangle, remembering that tan(theta) = opposite/adjacent

For Part B, just write taht because triangle XYZ was dilated with a scale factor of 2 to create triangle ABC, just multiply the sides by 2 to get the sides AC and CB

AC = 2 times XY

CB = 2 times YZ

and so from that, you should know how long AC and BC are

Sorry for  the long answer! Hope this helps though!

MrRoyal

The lengths of segments AC and CB are 5 and 10 units, respectively

How to determine the trigonometry relationships?

The given parameters are:

  • ΔXYZ [tex]\sim[/tex] ΔACB
  • Scale factor of dilation, k = 2
  • tan(X) = 5/2.5
  • ∠Y = ∠C = 90

Since the transformation is a dilation, it means that the triangles are similar, and the corresponding angles are equal.

So, we have:

X = A, Y = C and Z = B

Hence, the trigonometry relationships are tan(X) = tan(A), tan(Y) = tan(C) and tan(Z) = tan(B)

The values of segments AC and CB

In (A), we have:

tan(X) = 5/2.5

This means that:

tan(X) = YZ/XY

Substitute tan(X) = 5/2.5

YZ/XY = 5/2.5

By comparison, we have:

YZ = 5 and XY = 2.5

In (a), we have the corresponding points to be:

X = A, Y = C and Z = B

So, we have:

AC ⇒ XY ⇒ 2.5 * k

CB ⇒ YZ ⇒ 5 * k

This gives

AC = 2.5 * 2 = 5

CB =  5 * 2 = 10

Hence, the lengths of segments AC and CB are 5 and 10 units, respectively

Read more about similar triangles at:

https://brainly.com/question/14285697

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