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. pythagorean theorem (it depends on what you're missing..pythagorean theorem is c^2 = a^2 + b^2 where a and b are the legs and c is the hypotenuse)
2. yes you can...you use sin/cos/tan
3. yes you can...you use sin/cos/tan
4. special right triangles are the 30-60-90 and the 45-45 90

in 30-60-90 triangles the legs are always in the form of this:

hypotenuse = twice the length of the side opposite 30
side opposite 30 = 1/2 of the hypotenuse
side opposite 60 = the length of the side opposite 60 x sqrt 3

in 45-45-90

the sides opposite 45 are equal and they are equal to sqrt 2 times the hypotenuse

not sure about the last sentence...but i know that they are equal and there is a sqrt of 2 somewhere...just dunno if it's in the hypotenuse or the legs