Question

An equiangular triangle has one side of length six inches. What is the height of the triangle, drawn from that side, to the nearest tenth of an inch?
height =
in.

Answer 1

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Answer:

  5.2 in

Step-by-step explanation:

An equiangular triangle is also equilateral. All sides will be 6 inches, and the height line will be a perpendicular bisector of the side.

Using trig, the height is ...

  (3 in)tan(60°) = 3√3 in ≈ 5.2 in

Using the Pythagorean theorem, ...

  h² = 6² -3² = 27

  h = √27 ≈ 5.2 . . . inches