Tuesday, March 20, 2007
Geometry (Class 60)
Overview
We have seen that two right triangles are similar if one pair of angles, other than the right angles, are congruent. This means that all 40˚ right triangles, for instance, have the same ratios of sides-- Opposite/Hypotenuse, Adjacent/Hypotenuse, and Opposite/Adjacent being three key ratios. Today we extend the ratios we have calculated for 40˚ right triangles to all right triangles by compiling the data that the class created. We will then graph this data and put it to work solving right triangles.
Textbook Sections
§9.5 (Txt. p.558) Trigonometric Ratios
Key Attitudes
Mathematics is about justification.
Key Ideas
If two right triangles have one additional congruent pair of angles, then the triangles are similar.
If two right triangles are similar, then the ratios of their sides are equal.
If you know the measure of one non-right angle in a right triangle and the length of one side, then you can find the lengths of the other sides and the measures of the other angles.
If you know the length of two sides of a right triangle, then you can find the lengths of all of the sides of the right triangle.
A graph can be used to approximate values for trigonometric ratios.
Key Skills
Using trigonometric ratios to solve right triangles.
Writing and solving proportions.
Graphing data.
Using a graph to make predictions.
Vocabulary
trigonometric ratio
Handouts
No Handouts Posted
Assignment
§9.2 (Txt. p.538) #10-12, 18-21, 28, 31
§9.3 (Txt. p.546) #8-10, 16-19, 34
Finish graphs of trigonometric ratios from class
Quiz Corrections
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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