Question 255679
how do i do the 45 45 90 and the 30 60 90 triangles?

pythagorean theorem is for right triangle 
(triangles with a 90 degree angle as one of the 3 angles)

a^2+b^2=c^2  where a and b are 2 of the sides and c is the diagonal (longest side) otherwise known as the hypotenuse

45 45 90
take a rectangle and slice it in two at the diagonal and take one of the halves,
that is this triangle

length ^2 + width ^2 = diagonal ^ 2

30 60 90
that is half of an equalateral triangle (a triangle with 3 equal sides)

the short side will be half the base and will be opposite the 30 degree angle
the height will be opposite the 60 degree angle
the hypotenuse will be opposite the 90 degree angle

(1/2 base)^2 + height ^2 = hypotenuse ^2

you can also use these ratios to come up with the sides if you know the angle
sine
 opp/hyp
cosine
 adj/hyp
tangent
 opp/adj

the hypotenuse will always be opposite to the 90 degree angle

these are some of the ratios for these triangles
sine 45 = sqrt(2)/2 
sine 90 = 1
sine 30 = 0.5
sine 60 = sqrt(3)/2