Question

Each side of an equilateral triangle is 2. Find the length of an altitude

Answer 1

The length of an altitude in an equilateral triangle with each side of length 2 is √3, which is approximately 1.732 when rounded to three significant figures.

Step-by-step explanation:

To find the length of an altitude in an equilateral triangle with all sides of length 2, we can use the Pythagorean theorem. An altitude in an equilateral triangle also acts as the median, which means it splits the triangle into two 30-60-90 right triangles. Therefore, if we name the altitude h, one of the halves of the split base will be of length 1 (half of the original side length).

Using the Pythagorean theorem, we have

(1)2 + h2 = (2)2

Which simplifies to:

1 + h2 = 4

Solving for h:

h2 = 4 - 1

h2 = 3

h = √3 ≈ 1.732

So the length of the altitude is √3 or approximately 1.732, using three significant figures.