Geometry/Trig Notes

*Geometric Means Formulas:h= √xy (h is the altitude of the triangle)b= √xc ('x' is the side ADJACENT to b-usually underneath it. 'c' is the total of x+y)a= √yc (see above- it's the same principle for both a &b)*Pythagorean Triples:3,4,5 (& all multiples of each triple)5,12,138,15,177,24,25*Special Triangles:- 45-45-90 Triangle rules: ~hypotenuse= leg√2 ~legs are congruent, remember that this means 45-45-90 are isosceles-30-60-90 Triangle rules:~hypotenuse= 2(short side of the triangle*) (*the short side is ADJACENT to the SMALLEST ANGLE)~leg= short side√3*Sine, Cosine, Tangent, Secant, Co-secant, and Co-Tangent Ratios:sinX= opposite side/hypotenuse (o/h)cosX= adjacent side/hypotenuse (a/h)tanX= o/acsc= h/osec= h/acot= a/o(***When 'x' is a side length & you are given an angle measurement-use regular sin/cos/etc BUT IF YOU ARE LOOKING FOR THE ANGLE MEASURE PLUG THE RATIO INTO THE INVERSE FUNCTION OF SIN/COS/ETC****)*Law of Sines & Cosines -Law of Sines Formula:sinA/side a = sinB/side b = sinC/side c (remember to solve in proportions & that you can only solve two proportions at a time) -Law of Cosines Formulas: a^2= b^2+c^2-2bc(cos(A))b^2= a^2+c^2-2ac(cos(B)) c^2= a^2+b^2-2ab(cos(C))