Question

The side length of an equilateral triangle is 5 centimeters. Find the length of an altitude. Round your answer to the nearest tenth.

Answer 1

The side length of an equilateral triangle whose side length is approximately 4.3 centimeters.

Explanation:

By Geometry, we know that each internal angle in equilateral triangles equals 60º. Trigonometrically speaking, we remember that length of the altitude of an equilateral triangle (
`h`), in centimeters, is:

`h = l\cdot \sin 60^(\circ)` (1)

Where
`l` is the side length, in centimeters.

If we know that
`l = 5\,cm` and
`\sin 60^(\circ) = (√(3))/(2)`, then the height of the equilateral triangle is:

`h \approx 4.3\,cm`

The side length of an equilateral triangle whose side length is approximately 4.3 centimeters.