Transcript Chapter 9.1 Notes - Illini West High School Dist. 307

Chapter 8.1
Common Core G.SRT.8 & G.SRT.4 –
Use…Pythagorean Theorem to solve right
triangles in applied problems.
Objective – To use the Pythagorean Theorem
and its converse.
Chapter 8.1 Notes
Pythagorean Thm – a2 + b2 = c2
Pythagorean Triple – have to be natural numbers
3, 4, 5
5, 12, 13 7, 24, 25 8, 15, 17
a2 + b2 = c2
right triangle
a 2 + b 2 ⟨ c2
obtuse triangle
a 2 + b 2 ⟩ c2
acute triangle
Chapter 8.2
Common Core G.SRT.8 – Use…Pythagorean
Theorem to solve right triangles in applied
problems.
Objective – to use the properties of 45-45-90
and 30-60-90 degree triangles
Chapter 8.2 Notes
45° - 45 ° - 90 ° Triangles
30° - 60 ° - 90 ° Triangles
Chapter 8.3
Common Core G.SRT.8, G.MG.1, & G.SRT.7 –
Use trigonometric ratios and the Pythagorean
Theorem to solve right triangles in applied
problems. Use geometric shape, their
measures, and their properties to describe
objects.
Objective – To use the sine, cosine, and tangent
ratios to determine side lengths and angle
measures in right triangles.
Chapter 8.3 Notes
Trigonometric Ratios
SOH-CAH-TOA
Sin ∠ = _______
Cos ∠ = _______
Tan ∠ = _______
Trigonometric Ratios
Csc ∠ = _______ = _______
Sec ∠ = _______ = _______
Cot ∠ = _______ = _______
Sin
𝑂𝑝𝑝
∠=
𝐻𝑦𝑝
Cos
𝐴𝑑𝑗
∠=
𝐻𝑦𝑝
Tan ∠
𝑂𝑝𝑝
=
𝐴𝑑𝑗
Chapter 8.4
Common Core G.SRT.8 – Use trigonometric
ratios…to solve right triangles in applied
problems.
Objective – To use angles of elevation and
depression to solve problems.
Chapter 8.4 Notes
Angle of Elevation
Angle of Depression
These angles are always made from a horizontal line
Chapter 8.5
Common Core G.SRT.11 & G.SRT.10 –
Understand and apply the Law of Sines…to find
unknown measurements in right an non-right
triangles…
Objective – To apply the Law of Sines.
Chapter 8.5 Notes
Law of Sine
sin 𝐴
sin 𝐵
sin 𝐶
=
=
𝑎
𝑏
𝑐
C
b
A
a
c
B
Chapter 8.6
Common Core G.SRT.11 & G.SRT.10 –
Understand and apply the Law of Cosine…to find
unknown measurements in right an non-right
triangles…
Objective – To apply the Law of Cosine.
Chapter 8.6 Notes
Law of Cosine
𝑎2 = 𝑏2 + 𝑐 2 - 2bc Cos A
𝑏2 = 𝑎2 + 𝑐 2 - 2ac Cos B
𝑐 2 = 𝑎2 + 𝑏2 - 2ab Cos C
C
b
A
a
c
B