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GIVING 100 POINTS! pls help

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.

GIVING 100 POINTS pls help Part A Use complete sentences to explain the special relationship between the trigonometric ratios of triangles XYZ and ACB You must class=

Respuesta :

MisterBrainly

#Part A

As per Thales theorem

  • XY/AC=ZY/BC=XZ/AB=1/2(Given scale factor)

It simply means all the trigonometric ratios are same for both the triangles

#part B

  • tanX=5/2.5

YZ=5

XY=2.5

Now

  • XY/AC=1/2
  • 2.5/AC=1/2
  • AC=5

And

ZY=5

  • BC/ZY=2
  • BC=2ZY
  • BC=10
semsee45

Answer:

A)  In similar triangles, corresponding sides are always in the same ratio (see below for full explanation).

B)  AC = 5

    CB = 10

Step-by-step explanation:

Part A

Triangles XYZ and ACB are similar triangles as their corresponding angles are equal:

  • ∠X = ∠A
  • ∠Y = ∠C
  • ∠Z = ∠B

In similar triangles, corresponding sides are always in the same ratio.

⇒ XY : AC = YZ : CB = XZ : AB

Part B

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

  • [tex]\theta[/tex] is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

[tex]\sf \textsf{If } \:\tan X=\dfrac{5}{2.5}\:\:\textsf{ then}:[/tex]

  • O = YZ = 5 units
  • A = XY = 2.5 units

Given the scale factor is 1 : 2, set up an equation using the ratios described in part (a):

[tex]\implies \sf 1:2=XY:AC=YZ:CB[/tex]

[tex]\implies \sf \dfrac{1}{2}=\dfrac{XY}{AC}=\dfrac{YZ}{CB}[/tex]

[tex]\implies \sf \dfrac{1}{2}= \dfrac{2.5}{AC}=\dfrac{5}{CB}[/tex]

Solving for AC:

[tex]\implies \sf \dfrac{1}{2}= \dfrac{2.5}{AC}[/tex]

[tex]\implies \sf AC=2.5 \cdot 2=5[/tex]

Solving for CB:

[tex]\implies \sf \dfrac{1}{2}=\dfrac{5}{CB}[/tex]

[tex]\implies \sf CB = 5 \cdot 2 = 10[/tex]

Therefore:

  • AC = 5
  • CB = 10

Learn more about similar triangles here:

https://brainly.com/question/21427237

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