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What is the value of tan x? 3/5 5/4 3/4 4/3 4/5

What Is The Value Of Tan X 35 54 34 43 45 class=

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Answer:

[tex]\sf \tan(x)=\dfrac{4}{3}[/tex]

Step-by-step explanation:

Trigonometric ratios

[tex]\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\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
  • H is the hypotenuse (side opposite the right angle)

From inspection of the diagram:

  • [tex]\theta[/tex] = x
  • O = 8
  • A = 6
  • H = 10

[tex]\implies \sf \tan(x)=\dfrac{8}{6}=\dfrac{4}{3}[/tex]

[tex]\\ \rm\Rrightarrow tanx=\dfrac{Perpendicular}{Base}[/tex]

  • Perpendicular=8
  • Base=6

[tex]\\ \rm\Rrightarrow tanx=\dfrac{8}{6}[/tex]

[tex]\\ \rm\Rrightarrow tanx=\dfrac{4}{3}[/tex]

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