Question

What are the Special Right Triangles?

Answer 1

Special Right Triangles

1. `30^circ`-`60^circ`-`90^circ` Triangles whose sides have the ratio `1:sqrt{3}:2`

2. `45^circ`-`45^circ`-`90^circ` Triangles whose sides have the ratio `1:1:sqrt{2}`

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These are useful since they allow us to find the values of trigonometric functions of multiples of `30^circ` and `45^circ`.

Answer 2

There are 2 types of special right triangles.
Type 1. Triangle that is half of a equilateral triangle. Its 3 angle measures are: 30, 60 and 90 deg. Its side measures are : a, a/2; and (a*sqr.3)/2.
Type 2. Triangle that has its side measures in the ratio of 3:4:5. The proof is given by the Pythagor theorem: c^2 = b^2 + a^2.
Use of special right triangles.
In the old time, people use the special right triangles with sides ratio 3:4:5 to figure out, in the field, a right angle or a rectangular, or square, shape.
Now, students just use the properties of special right triangle to find, by computing, the unknown sides or angles.