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Introduction to Trigonometry Lesson 9.9 What is Trigonometry? • The shape of a right triangle is determined by the value of either of the other two angles. • This means that once one of the other angles is known, the ratios of the various sides are ALWAYS the same regardless of the size of the triangle. • These ratios are described by following “trigonometric functions” of the known angle. • This means that if one angle and one side length is known, all other angles and side lengths can be determined. • OR… it means that if two sides of the triangle are known, the third side and all other angles can be determined. Three Trigonometric Ratios B a c A b 1. Sine of A = sin A = opposite leg = a c hypotenuse b 2. Cosine of A = cos A = adjacent leg = c hypotenuse 3. Tangent of A = tan A = opposite leg = a adjacent leg b C S O H C A H T O A Sine Opposite Hypotenuse Cosine Adjacent Hypotenuse Tangent Opposite Adjacent Memorize this… Memorize this… S O H I N E P P O S I T E Y P O T E N U S E C A H T O A O S I N E D Y J P O A T C E E N N U S T E A N G E N T P P O S I T E D J A C E N T Find cos A 1. By the Pythagorean Theorem find side c. 2. c = 13 3. cos A = adjacent leg to A = 12 13 hypotenuse Find tan B 1. tan B = leg opposite B = 12 5 leg adjacent to B ΔABC is an isosceles triangle as marked. Find sin C. 1. Draw in an altitude to make a A right triangle. 25 25 2. Use the Pythagorean 20 Theorem to find the length of the altitude. B 15 30 15 3. AD = 20 4. Sin C = opposite = 20 = 4 hypotenuse 25 5 C Use the fact that tan 40º ≈ 0.8391 to find the height of the tree to the nearest foot. • Tan 40º = opposite = h adjacent 50 • 0.8391 ≈ h 50 • 0.8391(50) ≈ h • 41.955 ≈ h • The tree is ≈ 42 feet tall. Video Time…