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What is the height, $x$, of the equilateral triangle? A. 8 in. B. $8 \sqrt{3}$ in. C. 4 in. D. $4 \sqrt{3}$ in.

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Scott

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To find the height of an equilateral triangle, we can use the properties of 30-60-90 triangles. In an equilateral triangle, the height splits the triangle into two 30-60-90 triangles.

Solution By Steps

Step 1: Identify the sides of a 30-60-90 triangle

In a 30-60-90 triangle, the sides are in the ratio of 1:โˆš3:2. The shortest side is opposite the 30-degree angle, the middle side is opposite the 60-degree angle, and the longest side is opposite the 90-degree angle (the hypotenuse).

Step 2: Apply the ratio to the equilateral triangle

In an equilateral triangle, each side is equal. If we assume the side length of the equilateral triangle is

s, then the hypotenuse of the 30-60-90 triangle formed by the height is also

s. The height

x corresponds to the side opposite the 60-degree angle in the 30-60-90 triangle.

Step 3: Calculate the height

Using the ratio 1:โˆš3:2, if the hypotenuse (which is also a side of the equilateral triangle) is

s, then the height

x is

\frac{s\sqrt{3}}{2}.

Final Answer

The height

x of the equilateral triangle is

\frac{s\sqrt{3}}{2}. Without a specific value for

s, we cannot determine a numerical answer from the given options.

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