30-60-90 Triangles
Friday, November 15, 2013
10:09 AM
Slides
Notes
It can be handy to memorize the side lengths
of really common triangles and then you can
just use proportions to scale up or down to
find the side lengths for an unknown side in
another triangle.
The equilateral triangle is a no brainer. All
the sides are the same length, so long as you
have all 60 degree angles.
If you split that equilateral right down
through the middle, you have this handy
triangle. It isn't too hard to remember either.
The sides are 1, 2, and 3 - Well, OK, really it is
the square root of three, but it is still easy to
remember.
Now, let's put it all to work to find an
unknown side of another triangle. This one
tells you enough about the angles to confirm
that it is similar to your 30-60-90 triangle.
What is so neat is that all you need is just one
side and you can find another or even both
of the other two.
I like to jot down a note to myself as to which
I decided to put in the numerator and which
in the denominator. The first pair of ratios
Saxon 2_ 3rd ed Page 1
in the denominator. The first pair of ratios
will be from my memorized triangle. Since I
have been given the hypotenuse, I will need
that in there and then the side that matches
my y that I am solving for. That gives me a 2
over a 1. Now I will put in the ratios for the
hypotenuse in the second triangle and my
variable I am solving for. I will cross-multiply
and then divide. Y is 5/2.
Saxon 2_ 3rd ed Page 2