Mathematics

Question

Given the diagram below, what is the tan (60)?
Given the diagram below,  what is the tan (60)?

2 Answer

  • the sides of this triangle are in the ratio 2:1:sqrt3
    so the shorter of the 2 legs = 8  

    tan 60 = 8 sqrt3 / 8  = sqrt 3
  • Answer:

    B. [tex]\sqrt{3}[/tex]

    Step-by-step explanation:

    We have been given an image of a right triangle and we are asked to find the value of tan(60) for our given triangle.

    Since we know that tangent represents the relation between opposite and adjacent of right triangle.

    [tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

    We can see that our adjacent side is not given, but corresponding angle to adjacent side is given that is 30 degrees. So we can conclude that our given triangle is 30-60-90 triangle.

    Since the sides corresponding to 30-60-90 triangle equals to [tex] x,x\sqrt{3}\text{ and }2x[/tex], so the adjacent side for our given triangle will be:

    [tex]x\sqrt{3}=8\sqrt{3}[/tex]

    [tex]\frac{x\sqrt{3}}{\sqrt{3}}=\frac{8\sqrt{3}}{\sqrt{3}}[/tex]

    [tex]x=8[/tex]

    Upon substituting these values in above formula we will get,

    [tex]\text{tan}(60^o)=\frac{8\sqrt{3}}{8}[/tex]

    [tex]\text{tan}(60^o)=\sqrt{3}[/tex]

    Therefore, the value of tan(60) is [tex]\sqrt{3}[/tex] and option B is the correct choice.

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