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Law of Sines for Non-right Triangles

Learn how to use the Law of Sines to solve problems involving non-right triangles. This active learning assignment provides step-by-step instructions and practice questions.

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Law of Sines for Non-right Triangles

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  1. Got ID? 3-20-19 T3.1c To use the Law of Sines Get Handouts from the table at the door. Please be ready to start copying, we have bunches to do!!! Don’t say the answers out loud! Sound bites Fit as a fiddle Happy camper Cat scan

  2. OPENER: Start copying the text on this page: B c a h C A b * The Law of Sines: or You only use two ratios at a time. This is used for NON-RIGHT TRIANGLES!!!!!

  3. Active Learning Assignment Questions?

  4. B LESSON: a c h A C b The same proportion can be proved for A and B, and B and C This proportion is known as…

  5. B (This is the same as OPENER) AAS ASA SSA c a h C A b The Law of Sines: or You only use two ratios at a time. NON-RIGHT TRIANGLES!!! Write: YOU MUST HAVE AT LEAST ONE ANGLE AND ITS OPPOSITE SIDE KNOWN!!! What are the geometry relationships here?

  6. B (This is the same as OPENER) c a h C A b The Law of Sines: * or Write: The length of one side is to the sine of its opposite angle as any other side is to the sine of that opposite angle. In other words, if you divide out “a” and “sin A”, you will get the same value as dividing out “b” and “sin B”, etc.

  7. A simple example. Please set up and solve (1 dec. pl.): This is what we want to know This is a side that we know x 12 m Here is the angle opposite our known side. 57° 33° Here is the angle opposite our unknown side. (Don’t forget to close the parentheses!) 12 x sin 57° sin 57° sin 57° sin 33° The unknown side is 18.5 m.

  8. P 3000 yds. 63° 28° B S E Example: A ship passes by Buoy B which is known to be 3000 yds. from peninsula P. The ship is going east along line BE and ó PBE is 28°. After 10 minutes, the ship is at S and ó PSE is measured at 63°. How far is the ship from the peninsula when at S? (1 dec. pl.) What do we want to find? We must find the interior angle at S: What do we need? x 117° The ship is 1580.7 yds. away.

  9. Example: From points P and Q, 180 m apart, a tree at T is sighted on the opposite side of a ravine. Given the following information, how far is P from the tree? (1 dec. pl.) N N N T ravine x 27° 43° 78° Q P 180 m First, find the other angles. Angle P? 43° 27° 78° – 27° = 51° 70° Now, angle T: 27° + 43° = 70° Finally, angle Q: 59° 180° – (51° + 70°) = 59° 51° 164.2 m is the distance to the tree. Version 1

  10. N N T ravine x 27° 43° 78° Q P 180 m First, find the other angles. Another way to work it: Angle Q? 180° – (78° + 43°) = 59° Now, angle P: 70° 78° – 27° = 51° Finally, angle T: 180° – (59° + 51°) = 70° 59° 78° 51° PT is 164.2 m from the tree. Version 2

  11. C A B From your handout, work #19 as a group—Please read, fill in values, set up and solve (1 dec. pl.). What is the minimum requirement for the Law of Sines? What do we need to find, first? x The distance across the river is 118.0 m.

  12. Describe how you would know when to use the Law of Sines. Active Learning Assignment: Law of Sines Handout #20, 21, 22, 23, 25 (Answers on the handout) WOW: Life’s goals should be to become more civilized—don’t’ participate in “mob mentality.”

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