Geometry problem?

Question

For a equilateral triangle with sides measuring 14 cm each, how can you find the altitude of the triangle?

Answer 1

The altitude splits the equilateral triangle into two right triangles. The altitude is one leg. The other leg is half of 14 cm. and the hypotenuse is 14 cm.

By the Pythagorean theorem:
a² + 7² = 14²
a² = 196 - 49
a² = 147
a = sqrt(147)
a = sqrt(7 * 7 * 3)
a = 7 sqrt(3)

(Or if you remember the ratio of the sides of a 30-60-90 triangle are 1:2:sqrt(3) you can skip a few steps.)

The answer is 7 sqrt(3) ≈ 12.12 cm

Answer 2

the altitude = 7sqrt(3) cm
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Ideas: The altitude separates an equilateral triangle into two congruent 30-60-90 degree special triangles, in which the longer leg = sqrt(3) x the shorter leg.

Answer 3

Drop a perpendicular, (h), from apex on to base, making two congruent right angled triangles.

sin 60 = h/14, so

h = 14 sin 60, so

h = 14 x rt(3)/2, so

h = 7 rt(3)

Answer 4

7 sqrt 3