Altitude of an Equilateral triangle?

**captaintoast87** · February 26th 2009, 06:01 AM

We must have skipped over this in geometry. What's the formula to find the altitude? Thanks

**nmatthies1** · February 26th 2009, 06:21 AM

Let a be the length of a side of the equilateral triangle. Then altitude = $\sqrt {a^2-\frac{a^2} {4}} = \sqrt {\frac{3a^2} {4}}=\frac {a\sqrt{3}} {2}$

**HallsofIvy** · February 26th 2009, 07:23 AM

More precisely, if you draw a perpendicular from one vertex to the opposite side, it divides the side into two equal parts. If the equilateral triangle has side length s, then you have two right triangles with hypotenuse length s and one leg of length s/2. Use the Pythagorean theorem to find the length of the other leg, the altitude.

**HallsofIvy** · February 26th 2009, 07:25 AM

In general, if you draw a perpendicular from one vertex to the opposite side, it divides the side into two equal parts. If the equilateral triangle has side length s, then you have two right triangles with hypotenuse length s and one leg of length s/2. Use the Pythagorean theorem to find the length of the other leg, the altitude.

**sbcd90** · February 27th 2009, 10:20 AM

it is a*sin 60deg.

where,a is length of each side of equilateral triangle.

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