Hello,

So, I was puzzling over a math problem, when I noticed something interesting I wanted to share.

Imagine an equilateral triangle, the sides are all the same, as are the angles.

Let's say the side lengths are 1, and the angles are 60. The way people would normally find the height is to do the side squared minus the side divided by 2 squared, to equal the height squared.

In other words, The square root of (1^2 - 0.5^2)

This is where it got interesting:

The answer, or height, is 0.866025404

This got me thinking, and what if instead of doing The square root of (1^2 - 0.5^2) to find the height, what about taking the side and just multiplying it by 0.866025404?

I tried this out, this time with side lengths of 1.5. Both ways, with my method, and with the other method, I got the same answer for the height, which is 1.299038106.

It worked when I did The square root of (1.5^2 - 0.75^2), and when I did the side times 0.866025404.

In a nutshell, the side multiplied by 0.866025404. It's quicker, and just as accurate as the other method.

So, while trying to learn one thing, I learned something else!

HOWEVER, so far, it only works with triangles that have the same side length and the same angles. I am still experimenting with it, though.

That's what I learned today! I love geometry!

Jared

So, I was puzzling over a math problem, when I noticed something interesting I wanted to share.

Imagine an equilateral triangle, the sides are all the same, as are the angles.

Let's say the side lengths are 1, and the angles are 60. The way people would normally find the height is to do the side squared minus the side divided by 2 squared, to equal the height squared.

In other words, The square root of (1^2 - 0.5^2)

This is where it got interesting:

The answer, or height, is 0.866025404

This got me thinking, and what if instead of doing The square root of (1^2 - 0.5^2) to find the height, what about taking the side and just multiplying it by 0.866025404?

I tried this out, this time with side lengths of 1.5. Both ways, with my method, and with the other method, I got the same answer for the height, which is 1.299038106.

It worked when I did The square root of (1.5^2 - 0.75^2), and when I did the side times 0.866025404.

In a nutshell, the side multiplied by 0.866025404. It's quicker, and just as accurate as the other method.

So, while trying to learn one thing, I learned something else!

HOWEVER, so far, it only works with triangles that have the same side length and the same angles. I am still experimenting with it, though.

That's what I learned today! I love geometry!

Jared

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