Geometry/Trig Notes

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*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)

5,12,13

8,15,17

7,24,25

*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/a

csc= h/o

sec= h/a

cot= 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))