Friday, May 30, 2008
Geometry (Class 86)
Lesson Title
Law of Sines 4
Overview
The warm-up today requires that students apply their knowledge of the areas of polygons, angle relationships of polygons, and right triangle trigonometry to create a regular octagon with an area of 96 square cm.
We will then push on further into seeing the implications, and limitations, of the Law of Sines by working on Chapter 13- Lesson 2: Careful with the Law. As time permits we will begin our work to find a way to solve triangles for which the Law of Sines does not apply— The Law of Cosines!
Textbook Sections
Supplemental
Vocabulary
center
inscribed angle
central angle
radius (pl: radii)
chord
diameter
sections of intersecting chords
extended chords
inscribe
cyclic quadrilateral
law of sines
apothem
Key Attitudes
Math is about thinking creatively.
Key Ideas
The Law of Sines is a consequence of relationships between arcs and angles of circles.
Th eLaw of Sines can be sued to find missing side lengths or angle measures of triangle including those which are not right triangles.
The Law of Sines is a proportion stating that the ratio of the side length and the sine of the opposite angle is the same for all side/opposite angle pairs in any triangle.
For any obtuse angle their is a corresponding acute angle with the same sine.
In the case of knowing the measure of two sides and a non-included angle (SSA), the law of sines gives zero, one, or two possible solutions.
The law of sines can only be applied if the triangle in question has an angle and opposite side pair of measurements.
Key Skills
I can use right triangle trigonometry to solve a problem.
I can show how the Law of Sines is a consequence of the relationships between arcs, angles, and segment lengths in a circle.
I can use the Law of Sines to solve for missing length sides and angles in a triangle.
I can recognize a situation where using the Law of Sines would be useful.
I can translate a situation into an equation involving the Law of Sines and solve that equation.
I can recognize when I need to be extra careful with the Law of Sines.
I can create a regular polygon of a specified area.
Turn-In (#85)
Benchmark Test 4
Finish Chapter 13- Lesson 1: Law of Sines (Class Work)
Finish Chapter 13- Lesson 1: Law of Sines (Problems)
Test Corrections
Handouts
Areas of Regular Polygons Warm-Up
Chapter 13- Lesson 2: Being Careful with the Law
law of Cosines Problem 1
Chapter 13- Lesson 3: Law of Cosines
Benchmark Test 5 Answers
Assignment
Benchmark Test 5 (Skip #26)
Finish Area of Regular Polygon Warm-Up
Finish Chapter 13- Lesson 2: Careful with the Law
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.
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