Alt-On-Hyp, Trip and Similarity Flashcards

1
Q

Geometric Mean

A

x of a and b such that

x2 = ab

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2
Q

Alt-On-Hyp

A

The altitude to the hypotenuse of a right triangle is the geometric mean of the segments that the hypotenuse is divided into by the alititude

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3
Q

Leg-Alt-On-Hyp

A

If we draw an altitude to the hypotenuse of a right triangle, then each leg is the geometric mean of the hypotenuse and the adjacent segment of the hypotenuse

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4
Q

sin(x)

A

opposite leg

hypotenuse

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5
Q

cos(x)

A

adjacent leg

hypotenuse

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6
Q

tan(x)

A

opposite leg

adjacent leg

(slope of the hypotenuse)

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7
Q

sin(30°)

A

1/2

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8
Q

cos(30°)

A

sqrt(3)/2

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9
Q

tan(30°)

A

sqrt(3)/3

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10
Q

sin(60°)

A

sqrt(3)/2

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11
Q

cos(60°)

A

1/2

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12
Q

tan(60°)

A

sqrt(3)

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13
Q

sin(45°)

A

sqrt(2)/2

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14
Q

cos(45°)

A

sqrt(2)/2

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15
Q

tan(45°)

A

1

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16
Q

Law of Sines

A

sin(A) sin(B) sin(C)

———- = ——– = ——–

a b c

17
Q

Law of Cosines

A

a2 = b2 + c2 - 2bccosA

b2 = a2 + c2 - 2accosB

c2 = a2 + b2 - 2abcosC

18
Q

Identities with Supplementaries

A

sinA = sin(180-A)

-cosA = cos(180-A)

19
Q

Inverse Trig Functions

A

sin-1(opp/hyp) = x

cos-1(adj/hyp) = x

tan-1(opp/adj) =x

20
Q

To solve SSS and SAS

A

Use Law of Cosines

21
Q

To solve ASA, ASS and AAS

A

Use Law of Sines

22
Q

To solve HL

A

Use Pythag and Trig

23
Q

a < bsinA

A

No possible triangles

24
Q

a = bsinA

A

One possible triangle

25
Q

bsinA < a < b

A

two possible triangles

26
Q

a >/= b

A

one possible triangle