Day 5


Special Right Triangles

45-45-90 and 30-60-90

Let's look at the general case of a square to learn about 45-45-90 triangles.

From the Pythagoren Theorem,

And from this it proves our theorem, that in a 45-45-90 triangle, the hypotenuse is times as long as a leg.

Example:

What is the length of our hypotenuse? According to our theorem the hypotenuse is square root 2 times as long as a leg. So our hypotenuse is or about 11.3.

For a great 45-45-90 exercise of a baseball diamond click here.


There is a special relationship in a 30-60-90 triangle also.

If we draw an altitude from any vertex of an equilateral triangle, the triangle is then seperated into two congruent 30-60-90 triangles. Using the Pythagorean Theorem, it is possible to derive a formula relating the lengths of the sides to each other.

Let s = the measure of a side

Let a = the measure of the altitude

So we can see that in the 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg and the longer leg is suare root of 3 times as long as the shorter leg.


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Go on to Day 6