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

Trigonometry

Basic Ratios

Find the missing

Law of Sines

Law of Cosines

Special right

triangles

100 100 100 100 100

200 200 200 200 200

300 300 300 300 300

400 400 400 400 400

500 500 500 500 500

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

x2 = 302 + 212 –

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

Solve for x and y