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Lesson 9.5 Apply the Law of Sines

Lesson 9.5 Apply the Law of Sines. Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up. Lesson Presentation. Lesson Quiz. Warm-Up. Solve Δ XYZ. Warm-Up. Solve Δ ABC. 14. Vocabulary. Law of Sines:.

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Lesson 9.5 Apply the Law of Sines

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  1. Lesson 9.5Apply the Law of Sines Standard Accessed: Students will prove, apply, and model trigonometric functions and ratios. Warm-Up Lesson Presentation Lesson Quiz

  2. Warm-Up Solve Δ XYZ.

  3. Warm-Up Solve Δ ABC. 14

  4. Vocabulary Law of Sines: Can be used to solve triangles with no right angle, when two angles and the length of any side are known (AAS or ASA cases), or when the lengths of two sides and an angle opposite one of the two sides are known, (SSA).

  5. Essential Understandings When can the Law of sines be used to solve a triangle? • When two angles and the length of any side are known (AAS or ASA cases), or when the lengths of two sides and an angle opposite one of the two sides are known, (SSA). The law of sines is used to solve triangles with no right angle.

  6. 1 EXAMPLE Solve a triangle for the AAS or ASA case Solve ABC with and . SOLUTION 1. Draw a picture  2. Find the third angle, 3. Write the Law of Sine proportion 4. Write the Law of Sine proportion In ABC, and c.

  7. 1 EXAMPLE Solve a triangle for the AAS or ASA case Key Question When you are given the measures of two angles and one side of a triangle, why does it not matter whether the given side is the one included between the two angles? It does not matter since you are given the measures of any two angles, you can always find the third angle measure.

  8. Essential Understandings What are the possible triangles for the SSA case? • is obtuse & a b, one triangle • is acute & , one triangle • is acute & , one triangle • is acute & , Two triangles • Note: is always across from side a • Note: To find

  9. 2 EXAMPLE Solve the SSA case with one solution Solve ABC with and . SOLUTION 2. Draw a picture  1. Evaluate SSA case, a b & is obtuse, One triangle 3. Write the Law of Sine proportion 4. Find the third angle, 5. Write the Law of Sine proportion In ABC, and c.

  10. 3 EXAMPLE Examine the SSA case with no solution Solve ABC with and SOLUTION 2. Draw a picture  , a h 1. Evaluate SSA case, a b No solution (The triangle is not possible.) What will happen if you try to solve the triangle by applying the law of sines and using your calculator? Write the Law of Sine proportion Trying to find will give an ERROR message, since the value of the sine function is never greater than 1.

  11. 4 EXAMPLE Solve the SSA case with two solutions Solve ABC with and . 69 SOLUTION 2. Draw a picture  1. Evaluate SSA case, a b , a h Two possible triangles 3. Write the Law of Sine proportion 4. Find the third angle, 4. Find the third angle, 5. Write the Law of Sine proportion 5. Write the Law of Sine proportion

  12. Vocabulary Area of Triangle:

  13. 4 EXAMPLE Write and Solve a real – Use trig to find area of triangle KIS Vegetable Garden Esther and Frederick are setting up a triangular vegetable garden at KIS. They lay off lengths of 15ft and 11ft for two sides of the garden with a 62° angle between these two sides, what will be the area of the garden? SOLUTION 1. Draw a picture  2. Write an equation, The area of Esther’s and Frederick’s vegetable garden is 72.843.

  14. Lesson 9.5 Homework: • Practice B • Practice C “Honors”

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