Answer:
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.
