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9-5 Trigonometric Ratios

9-5 Trigonometric Ratios. A trigonometric ratio is a ratio of the lengths of 2 sides of a right triangle. You will learn to use trigonometric ratios of a right triangle to determine side length and angle measurement. Trigonometric Ratios.

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9-5 Trigonometric Ratios

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  1. 9-5 Trigonometric Ratios • A trigonometric ratio is a ratio of the lengths of 2 sides of a right triangle. • You will learn to use trigonometric ratios of a right triangle to determine side length and angle measurement.

  2. Trigonometric Ratios • Trigonometry is from the ancient Greek language and means “measurement of triangles”, and was first used in 1595. • The 3 basic ratios are sine,cosine and tangent. These are abbreviated as sin, cos, and tan respectively.

  3. Let ΔABC be a right triangle • The sine, cosine, and tangent of the acute angle A are defined as: Side opposite A Hypotenuse A Side adjacent A

  4. SOHCAHTOA!!! S = O/H C=A/H T=O/A

  5. Find the sine, cosine and tangent of a 30 angle. • Sketch a 30-60 -90 triangle. Use “1” as the length of the shorter leg. Therefore the hypotenuse will be 2 and the longer leg will be 13. 2 1 30 3 Note: Similar triangles always have the same trig ratios!!!!

  6. Indirect Measurements…again.  • You are measuring the height of a tree. You stand 45 feet from the base of the tree. You measure the angle of elevation from a point on the ground to the top of the tree to be 59(because you always carry around a clinometer, which allows you to do this). What trig ratio would use the known measures height and elevation? h 59 45ft

  7. Sin M  0.5812 Cos M  0.8137 Tan M  0.7143 Sin T  0.8137 Cos T  0.5812 Tan T  1.4 Sin A  0.7071 Cos A  0.7071 Tan A = 1 Sin N  0.7071 Cos N  0.7071 Tan N = 1 Sin Q = 0.8 Cos Q = 0.6 Tan Q  1.3333 Sin R = 0.6 Cos R = 0.8 Tan R = 0.75

  8. Find the value of each variable. Round decimals to the nearest tenth. 1. 2. x  10.4, y  6.7 x  1.7, y  4.7

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