A street sign company is making street signs in the shape of equilateral triangles. The side length of each sign is 22 inches. What is the exact altitude length so that the company will be able to know what size box to ship them in?

Answer: 11 sqrt3

Well, since this is an equilateral triangle, you know that all of the sides have the same length: 22 inches. If you want to find the altitude (height), you would have to use the Pythagorean theorem: a^2 + b^2 = c^2

This means that the sum of the two legs squared is equal to the hypotenuse of the triangle squared.

We already know that the hypotenuse is 22 inches, so we can plug that in as c.

We also know that to make the triangle a right triangle, we will need to halve the bottom side, getting 11 inches, which we can plug in as b.

Lastly, we need to know a, so that is our variable to solve (the height). Here is the equation:

a^2 + (11^2) = (22^2)

This is equal to:

a^2 + 121 = 484

Now subtract 121 from both sides to get a^2 on its own:

a^2 = 363

Lastly, take the square root of both sides to solve for a:

a = 11 sqrt3