Explore a world of knowledge and get your questions answered on IDNLearn.com. Join our knowledgeable community to find the answers you need for any topic or issue.

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?



Sagot :

  • 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]

View image Аноним
View image Аноним