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Natalija [7]
2 years ago
6

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?
​
SAT
1 answer:
Andreas93 [3]2 years ago
4 0
  • AC=Hypotenuse=20
  • BC=Base=16

AB:-

Apply Pythagorean theorem

\\ \rm\rightarrowtail P^2=H^2-B^2

\\ \rm\rightarrowtail P^2=20^2-16^2

\\ \rm\rightarrowtail P^2=400-256

\\ \rm\rightarrowtail P^2=144

\\ \rm\rightarrowtail AB=12

Now

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

Now

\\ \rm\rightarrowtail sinF=\dfrac{DE}{DF}

\\ \rm\rightarrowtail sinF=\dfrac{4}{6.6}

\\ \rm\rightarrowtail sinF=0.61

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