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31 October, 00:49

Triangle FGH is an equilateral triangle with sides measuring units.

What is the height of the triangle?

GR = units

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Answers (1)
  1. 31 October, 02:29
    0
    Draw an equilateral triangle FGH so that FH is the horizontal base. Draw a vertical line GR from G to line FH to represent the height of the triangle.

    Let a = length of a side of the equilateral triangle (all sides are equal).

    Each angle is 60° because the three angles add up to 180°.

    Let h = GR, the height of the triangle.

    Because the triangle is equilateral, triangle FGR is a right triangle, with

    m∠F = 60°,

    m∠R = 90°,

    FG = a.

    By definition,

    sin (F) = h/a

    That is,

    h = a*sin (F) = a*sin (60) = a * (√3/2).

    Answer:

    The height of the equilateral triangle is (a/2) √3,

    where a = length of a side of the triangle.
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