Holt McDougal Geometry 8-2 Trigonometric Ratios 8-2 Trigonometric Ratios Holt GeometryHolt McDougal Geometry

Holt McDougal Geometry

8-2 Trigonometric Ratios8-2 Trigonometric Ratios

Holt GeometryHolt McDougal Geometry


8-2 Trigonometric Ratios

Warm UpWrite each fraction as a decimal rounded to the nearest hundredth.

1. 2.

Solve each equation.

3. 4.





In trigonometry, the letter of the vertex of the angle is often used to represent the measure of that angle. For example, the sine of A is written as sin A.

Writing Math



Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.



Write the trigonometric ratio as a fraction and as a decimal rounded tothe nearest hundredth.



Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.

sin 52°

Be sure your calculator is in degree mode, not radian mode.

Caution!



Steps for using trigonometric ratios.

1.Circle ONE angle.

2.Label Opposite, adjacent, or hypotenuse.

3.Use SOHCAHTOA



Find the length. Round to the nearest hundredth.

BC



Do not round until the final step of your answer. Use the values of the trigonometric ratios provided by your calculator.

Caution!




QR




FD




DF




ST




BC




JL

















Example 5: Problem-Solving Application

The 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?



A flagpole is held upright by 30m long wires to the ground. If the wires make an angle of 25 degrees to the ground, how high is the flagpole?



A surveyor wants to the measure the width of a river at point A. She places stakes 100 feet apart on the far side of the river and she is standing at point A. She finds that the measurement of angle BAC is 27 degrees and ABC is 90 degrees. How wide is the river?



Lesson Quiz: Part I

Use a special right triangle to write each trigonometric ratio as a fraction.

1. sin 60° 2. cos 45°

Use your calculator to find each trigonometric ratio. Round to the nearest hundredth.

3. tan 84° 4. cos 13°



Lesson Quiz: Part II

Find each length. Round to the nearest tenth.

5. CB

6. AC

Use your answers from Items 5 and 6 to write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.

7. sin A 8. cos A 9. tan A

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Holt McDougal Geometry 8-2 Trigonometric Ratios 8-2 Trigonometric Ratios Holt GeometryHolt McDougal Geometry