 # Trigonometry. Basic Ratios Find the missing Law of Sines Law of Cosines Special right triangles 100 200 300 400 500.

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Trigonometry

Basic Ratios Find the missing Law of Sines Law of Cosines Special right triangles 100 200 300 400 500

What is the acronym we use to remember trig functions?

SOH CAH TOA

Sin θ

Sin θ = 5/13

Tan θ=6/8=3/4

Write the ratio you would use to find x

Cos θ = x / 11

What ratio would you create given the information?

Cos θ = 4 / 5

Find x

Tan 32 = x / 13 X = 8.1°

Find x

Cos 37 = 11 / x X = 13.7

Find θ

Cos -1 ( 4.4/11) θ = 66.4°

Find θ

Tan -1 ( 7.7 / 14) θ = = 28.8°

Find all the missing parts of the triangle

What is the law of sines?

Sin A = Sin B = Sin C a b c

Set up the ratio for AB in the following triangle

Sin 53 = Sin 44 X 7

Solve for angle b

Sin b = Sin 115 16 123 B = 6.8°

Find BC

Sin 29 = Sin 93 16 X X = 33

Draw the triangle. Solve for the missing pieces m ∠ C = 145° b = 7 c = 33

m ∠ A = 28° m ∠ B = 7° a = 27

What is the traditional law of cosines?

Set up the formula to find BC

x 2 = 30 2 + 21 2 – 2(30)(21)cos123

Solve for AB

AB = 21

Find the measure of angle A

A = 137°

Solve the triangle

What are the two special right triangles?

30 – 60 – 90 45 – 45 – 90

What is the relationship between the side lengths in a 45 – 45- 90 triangle?

The legs are the same The hypotenuse is Leg√2

What is the relationship between the side lengths of a 30 – 60 – 90 triangle?

Long leg = SL√3 Hypotenuse = 2 * SL

Solve for x and y

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