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Notes # ____ 12.4 Tangent Ratio

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**Vocabulary trigonometry : the study of the properties of triangles**

trigonometric ratio : ratio of measures of two sides of a right triangle tangent : in a right triangle, the ratio of the leg opposite the acute angle to the leg adjacent to the acute angle

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Definition A C B hypotenuse leg adjacent to A leg opposite A

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Ex 1 Find tan A and tan B. A C B 41 40 9

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Ex 2 Find tan P and tan Q. P R Q 5 4 3

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**Tangents with Angle Measurements**

Ex 3 Tangents with Angle Measurements Find the measurement of DF. The tangent of an angle depends on the angle, not the size of the triangle. F D E 70 45 m

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Ex 4 Find the measurement of QR. R Q P 55 20 m

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**Angles of Elevation and Depression**

Find the measurement of DF. Applications of trigonometry may include these angles angle of depression angle of elevation

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Ex 5 Find the height of the tree C A 5 ft 40 B 100 ft

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**Ex 6 Find the angle of elevation.**

arctangent is the same as inverse tangent C 10 ft B 48 ft A

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Ex 7 Find the angle of depression. C 760 ft B 5000 ft A

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