Trigonometry. Basic Ratios Find the missing Law of Sines Law of Cosines Special right triangles 100...
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Transcript of Trigonometry. Basic Ratios Find the missing Law of Sines Law of Cosines Special right triangles 100...
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