mathdude0024
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In triangle ABC, the measure of ∠B is 90°, BC=16, and AC=20. Triangle DEF is similar to triangle ABC, where vertices D, E, and F correspond to vertices A, B, and C, respectively, and each side of triangle DEF is 1/3 the length of the corresponding side of triangle ABC. What is the value of sinF?

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Respuesta :

  • AC=Hypotenuse=20
  • BC=Base=16

AB:-

Apply Pythagorean theorem

[tex]\\ \rm\rightarrowtail P^2=H^2-B^2[/tex]

[tex]\\ \rm\rightarrowtail P^2=20^2-16^2[/tex]

[tex]\\ \rm\rightarrowtail P^2=400-256[/tex]

[tex]\\ \rm\rightarrowtail P^2=144[/tex]

[tex]\\ \rm\rightarrowtail AB=12[/tex]

Now

  • DE=AB/3=12/3=4
  • EF=BC/3=16/3=5.3
  • DF=AC/3=20/3=6.6

Now

[tex]\\ \rm\rightarrowtail sinF=\dfrac{DE}{DF}[/tex]

[tex]\\ \rm\rightarrowtail sinF=\dfrac{4}{6.6}[/tex]

[tex]\\ \rm\rightarrowtail sinF=0.61[/tex]

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