Geometry BName:______________________ Date: ___________

Chapter 8: Right Triangles & Trigonometry Section 8.2: Trigonometric RatiosAre you ready? Do this for homework!!!Write each fraction as a decimal rounded to the nearest hundredth.

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Solve each equation.

3) 4)

Objectives of Lesson: TSW find the sine, cosine, and tangent of an acute angle. TSW use trigonometric ratios to find side lengths in right triangles and to solve real-world problems. When would I ever use this? Contractors use trigonometric ratios to build ramps that meet legal requirements.A trigonometric_____________________________________________ _____________ ____________________________________________ __________________________________________________________________________________________________________________

Writing Math: ____________________________________________

___________________________________________________________________________________________________________________________________________________________________________ Example 1: Finding Trigonometric RatiosWrite the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.sin J

Example 2: Finding Trigonometric RatiosWrite the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.cos J

Example 3: Finding Trigonometric RatiosWrite the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.tan K

Example 4: Finding Trigonometric RatiosWrite the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.cos A

Example 5: Finding Trigonometric RatiosWrite the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.tan B

Example 6: Finding Trigonometric RatiosWrite the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.sin B

Example 7: Finding Trigonometric Ratios in Special Right TrianglesUse a special right triangle to write cos 30° as a fraction.

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Example 8: Finding Trigonometric Ratios in Special Right TrianglesUse a special right triangle to write tan 45° as a fraction..

Example 9: Calculating Trigonometric RatiosUse your calculator to find the trigonometric ratio. Round to the nearest hundredth.sin 52°

Example 10: Calculating Trigonometric RatiosUse your calculator to find the trigonometric ratio. Round to the nearest hundredth.cos 19°

Example 11: Calculating Trigonometric RatiosUse your calculator to find the trigonometric ratio. Round to the nearest hundredth.tan 65°

Example 12: Calculating Trigonometric RatiosUse your calculator to find the trigonometric ratio. Round to the nearest hundredth.tan 11°

Example 13: Calculating Trigonometric RatiosUse your calculator to find the trigonometric ratio. Round to the nearest hundredth.tan 62°

Example 14: Calculating Trigonometric RatiosUse your calculator to find the trigonometric ratio. Round to the nearest hundredth.

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cos 30°

Example 15: Using Trigonometric Ratios to Find LengthsFind the length. Round to the nearest hundredth.BC

Caution:_____________________________________________________________________________________________________________________________________________________________________Example 16: Using Trigonometric Ratios to Find LengthsFind the length. Round to the nearest hundredth.QR

Example 17: Using Trigonometric Ratios to Find LengthsFind the length. Round to the nearest hundredth.FD

Example 18: Using Trigonometric Ratios to Find LengthsFind the length. Round to the nearest hundredth.DF

Example 19: Using Trigonometric Ratios to Find LengthsFind the length. Round to the nearest hundredth.ST

Example 20: Using Trigonometric Ratios to Find LengthsFind the length. Round to the nearest hundredth.

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BC

Example 21: Using Trigonometric Ratios to Find LengthsFind the length. Round to the nearest hundredth.JL

Example 22: Problem-Solving ApplicationThe Pilatusbahn in Switzerland is the world’s steepest cog railway. Its steepest section makes an angle of about 25.6º with the horizontal and rises about 0.9 km. To the nearest hundredth of a kilometer, how long is this section of the railway track?

Example 23: Problem-Solving ApplicationA contractor is building a wheelchair ramp for a doorway that is 1.2 ft above the ground. To meet ADA guidelines, the ramp will make an angle of 4.8° with the ground. To the nearest hundredth of a foot, what is the horizontal distance covered by the ramp?

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