Download Counting Techniques Investigation

PreCalculus
Law of Sines Activity: Oblique Triangles
Name____________________________ #______
In this investigation you’ll explore a special relationship between the sines of the angle measures of an oblique triangle and the length of
the sides.
1.
Have each group member draw a different acute triangle ABC . Label the length of the side opposite  A as a,
the length of the side opposite  B as b, and the length of the side opposite  C as c. Draw the altitude from
 A to BC . Label the height h.
2. The altitude divides the original triangle into two right triangles, one containing  B and the other
containing  C . Use your knowledge of right triangle trigonometry to write an expression involving sin B and h,
and an expression with sin C and h.
3. Combine the two expressions by eliminating h. Write your new expression as a proportion in the form
sin B sin C
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4. Now draw the altitude from  B to AC and label the height j. Repeat Step 3 using expressions involving j,
sin C and sin A . What proportion do you get when you eliminate j?
5. Compare the proportions that you wrote in Steps 3 and 4. Use the transitive property of equality
(If a = b and b = c, then a = c) to combine them into an extended proportion:
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 
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6. Share your results with the members of your group. Did everyone get the same proportion in Step 5?
Kamischke, Ellen, Eric Kamischke, and Jerald Murdock, Discovering Algebra: An Investigative Approach 2nd Edition. Emeryville: Key Curriculum, 2007. p. 468-469.