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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 ? ? 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: ? ? ? ? ? ? 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.