Question

1. If I know the lengths of two sides of a right triangle, how do I find the third?
2. Could I find the two missing side lengths of a right triangle if I only know one side length and one angle measure (other than the 90 degree angle)?
3. Could I find the two missing angle measures if I know some of the side lengths of a right triangle?
4. What makes a triangle a “special” right triangle? How can special right triangles help me find side lengths?

Answer 1

1. c² = a² + b²
2. yes. http://www.mathsisfun.com/algebra/trig-finding-side-right-triangle.html
3. If you have the lengths of the sides of the triangles you can use Sin/Cos/Tan to find the missing angles
4. There can be infinite right triangles but there are a few right triangles where finding the sides is quite easy. Like a right triangle with the other two angles equal that's 45 each. So the other two sides will be equal and third side is hypotenuse.
Or the right triangle with sides 3,4 5 where \[5^2=3^2 + 4^2\]
or 8,15 and 17 where \[17^2 = 8^2 + 15^2\]

and so on. Here it's easy to find the sides. These are special right triangles

this is a very helpful website: http://www.mathsisfun.com/algebra/trigonometry.html