1. Grade 10 Academic (MPM2D) Unit 6: Trigonometry 2: Non-Right Triangles Sine Law
Mr. Choi
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2. Trigonometry is a branch of mathematics that studies the relationship between the measures of the angles and the lengths of the sides in triangles.
Sine Law
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3. Notation: In any triangle, the vertices are named using capital letters as in the given example. The lengths of the sides are named using lower case letters that match the opposite vertex.
Sine Law
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4. Sine (Sin), COSINE (Cos), TANGENT (Tan):
Opposite side
Adjacent side
Hypotenuse side
Sine Law
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5. Earlier you explored the relations between the angle measures and sides of right triangles. You developed ratios of the lengths of the sides of similar triangles and called these trigonometric ratios sine, cosine, and tangent. Of course, not all real-world situations can be modelled with right triangles. Other methods must be found to solve problems that involve general, non-right triangles.
Sine Law
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6. Investigations Given , complete the chart below
What do you notice?
The trigonometric ratios between the angle and corresponding side are same.
80o
65o
35o
8.7 cm
8 cm
5 cm
0.11
0.11
0.11
Accurate to 2 decimal places
Sine Law
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7. Non-right triangles Sine Law
Trigonometric Ratios are no longer work for non-right triangles
Instead:
Sine law and Cosine law
Sine Law or
Similar idea for A
Sine Law
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8. Example 1: Sine Law Given the diagram of ABC, A = 71. 2°, B = 63
Example 1: Sine Law Given the diagram of ABC, A = 71.2°, B = 63.7°, and a = 75cm. Solve the triangle.
71.2° b c
Supplementary Angles
Sine Law
63.7°
75 cm
Reference Ratio
Sine Law
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9. Example 2: Given the diagram of DEF, F = 35°, f = 42 m, and d = 64 m
Example 2: Given the diagram of DEF, F = 35°, f = 42 m, and d = 64 m. Solve the triangle. (1 decimal place for side, nearest degree for angles)
Sine Law e
Reference Ratio
42 m
35°
64 cm
Supplementary Angles
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Sine Law

10. Sine Law Supplementary Angles Therefore total fencing needed:
Example 3: The town surveyor has to stake the lot market for a new public park beside an existing building lot. The engineering department gave this sketch. How much chain-link fence will be needed to enclose the entire park?
Supplementary Angles
Sine Law
Reference Ratio
Therefore total fencing needed:
= 46.0m m m
= 127.3m
Sine Law
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11. Homework
Work sheet: Day 1: Sine Law Text: Day 2: P. 549 #1-4, 6-8 P. 550 #10, 15 P. 555 #1, 5, 9, 12 Check the website for updates
Sine Law
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12. End of lesson
Sine Law
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