What is the length of the altitude of the equilateral triangle below

Step-by-step explanation:

Recall that an equilateral triangle has three equal interior angles, all 60°.  Let b represent the length of the base.  Draw a dashed line from the upper vertex to the base, perpendicularly.  This dashed line represents the height or altitude of the triangle.  

Now construct a triangle whose opposite side is this altitude, whose hypotenuse is b (and whose base is (1/2)b).

The altitude (opp) is then given by sin Ф = opp / hyp = opp / b.  Solving this for the altitude (opp), we get b·sin 60°:

alt (opp)       √3

=

  hyp             2

                                                b·√3    

so that 2 alt = b·√3, or alt =

                                                    2

Thus, for any equilateral triangle of side length b, the height of the triangle is

                             √3

alt = height = b ·

                               2

Please note:  Your problem statement refers to "the equilateral triangle below."  It's important that you share such illustrations, along with all instructions.  In this case your question was general enough so that I could use the definitions of "sine," "equilateral," etc., to come up with a general answer.

f(x) is the value of the function. b is the value of the function when x equals zero or the y-coordinate of the point where the line crosses the y-axis in the coordinate plane.

step-by-step explanation:

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