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MPM2D Unit #8 - Lesson #1 8.1/8.2 - The Sine Law Recall: We can only use PRIMARY TRIGONOMETRIC RATIOS when working with ________ triangles. Now we will be working with non-right triangles, also known as ____________ triangles. GOAL: Explore the relationship between each side in an acute triangle and the sine of its opposite angle. Discovering the Sine Law: Steps 1. Start with acute ΔABC. 2. Since the primary trig ratios are only used for right triangles, draw a ________________ ____________, AD, from A to BC to form ____ right triangles, Δ ABD and Δ ACD 3. Write equations for the SINES of <B and <C in the 2 right triangles. 4. Isolate side AD in both equations from step 3. 5. Set the expressions for AD _______ to one another. 6. Write each side of the equation as a ratio with information about only ONE triangle. (Bring everything about “B” together and everything about “C” together) MPM2D Unit #8 - Lesson #1 7. Divide Δ ABC differently so that we can use < A. Draw height BE from B to AC to create another 2 right triangles: Δ ABE and Δ CBE. 8. Write equations for the SINES of <A and <C in the 2 right triangles. 9. Isolate side BE in both equations from step 8. 10. Set the expressions for BE _______ to one another. 11. Write each side of the equation as a ratio with information about only ONE triangle. (Bring everything about “A” together and everything about “C” together) 12. Write a final statement comparing all 3 ratios. This is the _______ _______. Sine Law in any _________ triangle, you can use the following to calculate unknown _______ lengths and ________ measures: MPM2D Unit #8 - Lesson #1 GOAL: Use the sine law to calculate unknown side lengths and angle measures in acute triangles. To use the SINE LAW to determine a side length of angle measure, use these steps: o Determine the ratio of the sine of a __________ angle measure and a _________ side length. o Create an ______________________ ratio using either: The ____________ side length and the measure of its KNOWN opposite angle OR The sine of an ____________ angle measure and the KNOWN length of its opposite side. o __________ the ratios you created, and SOLVE for the unknown value. Example: Determine the length of AC to the nearest metre. Example: In Δ DST, ∠ D = 47°, d = 78 cm, and s =106 cm. Determine the measure of ∠S to the nearest degree. MPM2D Unit #8 - Lesson #1 Example: Determine the indicated angle measures for Δ QRS. You Try! Sine Law TWO known sides and the angle that is _________ one of these sides TWO known angles and ANY one _______ EXIT SLIP: Solve for “c” using the Sine Law. Homework: pg. 427 #2, pg. 433 - 434, # 2, 3abcf, 5, 6