Math Is Fun Forum

zoe

Guest

special right triangle....geometric mean what?

please someone explain geometric mean, 30-60-90, and 45-45-90

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: special right triangle....geometric mean what?

You get the geometric mean of a set of numbers by multiplying them all together and then taking the nth root of them, if there are n numbers.

For example, let's say you have the numbers 4, 9 and 16.
Multiplying all of those together gives 576, and there are 3 numbers so you would take the third root of that to get the geometric mean. This is roughly 8.32.

The 30-60-90 and 45-45-90 are special types of right-angled triangles that you can use to work out the sin, cos and tan of certain angles.

The shortest side of a 30-60-90 triangle is exactly half the length of its hypotenuse, and so:
sin (30) = cos (60) = 1/2
sin (60) = cos (30) = √(3)/2.

tan = sin/cos, and so you can use the above results to find tan (30) and tan (60) as well.

The two small sides of a 45-45-90 are equal, and using Pythagoras you can work out the hypotenuse of that triangle to be √(2) times the length of one of the other sides.

Therefore, sin (45) = cos (45) = 1/√(2), and so tan (45) is clearly 1.

---

Why did the vector cross the road?
It wanted to be normal.