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Geometry 7.6

Geometry 7.6. Apply the Sine and Cosine ratio. How Leg lengths relate to interior Angles. HYPOTENUSE. OPPOSITE. . ADJACENT. Trigonometric Functions.

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Geometry 7.6

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  1. Geometry 7.6 Apply the Sine and Cosine ratio

  2. How Leg lengths relate to interior Angles

  3. HYPOTENUSE OPPOSITE  ADJACENT Trigonometric Functions If you are given lengths of sides of a right triangle, the trigonometric functions sine, cosine, and tangent relate the interior angles to the ratio of the specified triangle lengths.

  4. HYPOTENUSE OPPOSITE  ADJACENT What does sine, cosine, and tangent give? If you know two lengths of a right triangle you can determine the third by the pythagorean theorem. Since the interior angle is directly related to the ratio of sides, you only need one length and one acute angle to determine the lengths of the other sides.

  5. SOH CAH TOA – the sine function To use the sine function you need to use the interior angle as an input. The output then gives you the ratio of the length of the opposite side to the hypotenuse. If you know either the opposite side or the hypotenuse, you can determine the unknown length.

  6. Finding Lengths in Right Triangles using the sine function Example: To find y, use the sine trigonometric function. 10 y 40o , so y=10sin(40o)=10(.6427)=6.427

  7. SOH CAH TOA – the cosine function To use the cosine function you need to use the interior angle as an input. The output then gives you the ratio of the length of the adjacent side to the hypotenuse. If you know either the adjacent side or the hypotenuse, you can determine the unknown length.

  8. 10 40o x Finding Lengths in Right Triangles using the cosine function Example: To find x, use the cosine trigonometric function. , so x = 10cos(40o)=10(.7660)=7.660

  9. Remember trigonometric functions give ratios output decimal input angle (in degrees)

  10. B 3 C A 4 What if you know the length of 2 sides, but don’t know the angles? What is mA? You don’t have the angle, but you do have the ratio of opposite side/adjacent side. therefore

  11. B 3 C A 4 What if you know the length of 2 sides, but don’t know the angles? You want A, which is an input to a function, so you must “undo” the tangent function (take its inverse). This is called the arc trig function And is written as

  12. Inverse trig functions output angle (degrees) input ratio (decimal)

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