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# MWA10 7.2 Sine Ratio

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# MWA10 7.2 Sine Ratio

MWA10 7.2 Sine Ratio

MWA10 7.2 Sine Ratio

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### MWA10 7.2 Sine Ratio

1. 1. The Sine Ratio Slide 1 In the previous lesson, you used the Pythagorean Theorem to find the measure of a missing side (of a right triangle). Over the next few lessons, you will learn different methods for finding the measure of a side or an angle. How to label triangles: •  (theta) – usually used to identify an angle (a capital letter can also be used to identify an angle) • adjacent – the side that is adjacent to the angle • opposite – the side that is opposite to the angle • hypotenuse – the side that is directly across from the right angle.
2. 2. Slide 2 When labelling the right triangle, everything depends on which angle you plan to work with. Reminder: • adjacent – the side that is adjacent to the angle • opposite – the side that is opposite to the angle • hypotenuse – the side that is directly across from the right angle. A B C  A B C  opposite opposite
3. 3. Slide 3 When labelling the right triangle, everything depends on which angle you plan to work with. Reminder: • adjacent – the side that is adjacent to the angle • opposite – the side that is opposite to the angle • hypotenuse – the side that is directly across from the right angle. A B C  A B C  adjacent adjacent
4. 4. Slide 4 Tip to help remember which side is which. Straight line across from angle = opposite (P has a straight line as part of its shape) Curved line from angle = adjacent (J is a curved letter) A B C  A B C  adjacent opposite opposite adjacent
5. 5. Slide 5 Calculator Check … When working with the trigonometric ratios: sine, cosine and tangent, you must make sure your calculator is set to Degree Mode. Quick Check: sin 30 = 0.5 If you do not get this as an answer, then your calculator is not in degree mode.
6. 6. Slide 6 The Sine Ratio Formal definition: in a right triangle, the ratio of the length of the side opposite a given angle to the length of the hypotenuse A B C  sin opp hyp   adjacent opposite
7. 7. Example 1: PQR is shown below. Using the SINE ratio, find the measure of x (round to 1 decimal place). Slide 7 x 67 120
8. 8. Example 1: PQR is shown below. Using the SINE ratio, find the measure of x (round to 1 decimal place). Slide 8 x 67 120 Label the triangle. Identify the formula. adjacent opposite hypotenuse sin opp hyp  
9. 9. Example 1: PQR is shown below. Using the SINE ratio, find the measure of x (round to 1 decimal place). Slide 9 x 67 120 Label the triangle. Identify the formula. adjacent opposite hypotenuse sin opp hyp   sin 67 120 x  0.9205 120 x  *Recommendation: Use 4 decimal places  0.9205 1 120 1 0 20 2 x       110.46 110.5 x x   
10. 10. Example 2: PQR is shown below. Using the SINE ratio, find the measure of x (round to 1 decimal place). Slide 10 5 23 x
11. 11. Example 2: PQR is shown below. Using the SINE ratio, find the measure of x (round to 1 decimal place). Slide 11 5 23 x Label the triangle. Identify the formula. sin opp hyp   adjacent opposite hypotenuse 5 sin 23 x  5 0.3907 x  *Recommendation: Use 4 decimal places   5 0.3907 x x x        0.3907 5x  0.3907 0.3907 07 5 0.39 x  12.7975 12.8 x x  
12. 12. Slide 12 New Terms: Angle of Elevation Angle of Depression When you look up at an airplane flying overhead, the angle between the horizontal and your line of sight is called an angle of elevation. When you look down from a cliff to a boat passing by, the angle between the horizontal and your line of sight is called an angle of depression.
13. 13. Example 3: The angle of elevation of Sandra’s kite string is 70. If she has let out 55 feet of string, and is holding the string 6 feet above the ground, how high is the kite? Slide 13
14. 14. Example 3: The angle of elevation of Sandra’s kite string is 70. If she has let out 55 feet of string, and is holding the string 6 feet above the ground, how high is the kite? Slide 14 Label the triangle. Identify the formula. sin opp hyp   adjacent oppositehypotenuse
15. 15. Example 3: The angle of elevation of Sandra’s kite string is 70. If she has let out 55 feet of string, and is holding the string 6 feet above the ground, how high is the kite? Slide 15 Label the triangle. Identify the formula. sin opp hyp   adjacent oppositehypotenuse sin 70 55 h  0.9397 55 h   0.9397 5 55 55 5 h       51.6835 51.7 51.7 57.7 6 h h h h feet      *Held 6 feet above ground