1 / 11

§10.6 Trigononmetric Ratios

§10.6 Trigononmetric Ratios. A H. O H. O A. Let c = , s = , t = . Calculate c , s , and t for the given values. 1. A = 3, O = 4, H = 5 2. A = 5, O = 12, H = 13 Solve each equation. 3. = 4. = 5. = 6. = . 0.34 1. 15 x. 0.75 1. x

khoi
Download Presentation

§10.6 Trigononmetric Ratios

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. §10.6 Trigononmetric Ratios

  2. A H O H O A Let c = , s = , t = . Calculate c, s, and t for the given values. 1.A = 3, O = 4, H = 5 2.A = 5, O = 12, H = 13 Solve each equation. 3. = 4. = 5. = 6. = 0.34 1 15 x 0.75 1 x 20 x 0.52 14 1 0.84 1 21 x Warm-Ups

  3. 1. For A = 3, O = 4, H = 5: c = = , s = = , t = = 2. For A = 5, O = 12, H = 13: c = = , s = = , t = = 3. = 4. = 0.75x = 15 x = 20(0.34) x = 20 x = 6.8 5. = 6. = 0.84 = 21 x = 14(0.52) x = 25 x = 7.28 1. For A = 3, O = 4, H = 5: c = = , s = = , t = = 2. For A = 5, O = 12, H = 13: c = = , s = = , t = = 3. = 4. = 0.75x = 15 x = 20(0.34) x = 20 x = 6.8 5. = 6. = 0.84 = 21 x = 14(0.52) x = 25 x = 7.28 A H A H 3 5 3 5 O H O H 4 5 4 5 O A O A 3 4 3 4 A H A H O H O H O A O A 5 13 5 13 12 13 12 13 12 5 12 5 0.34 1 0.34 1 x 20 x 20 15 x 15 x 0.75 1 0.75 1 0.84 1 0.84 1 21 x 21 x x 0.52 x 0.52 14 1 14 1 Solutions

  4. opposite leg hypotenuse opposite leg adjacent leg 6 10 3 5 sin A = = = adjacent leg hypotenuse 8 10 4 5  cos A = = = 6 8 3 4   tan A = = = Example 1: Finding Trigonometric Ratios Use the triangle. Find sin A, cosA, and tan A.

  5. To find sin 40°, press 40 . Use degree mode when finding   trigonometric ratios. Example 2: Finding a Trigonometric Ratio Find sin 40° by using a calculator. Rounded to the nearest ten-thousandth, the sin 40° is 0.6428.

  6. adjacent leg hypotenuse cos 30° = x 15 cos30° = Substitute x for adjacent leg and 15 for hypotenuse. 15 30 12.99038106 Use a calculator. x 13.0 Round to the nearest tenth. Example 3: Finding a Missing Side Length Find the value of x in the triangle. Step 1:Decide which trigonometric ratio to use. You know the angle and the length of the hypotenuse. You are trying to find the adjacent side. Use the cosine. Step 2: Write an equation and solve. x = 15(cos 30°) Solve for x. The value of x is about 13.0.

  7. Draw a diagram.  Example 4: Finding the Measures of an Angle Suppose the angle of elevation from a rowboat to the top of a lighthouse is 70o. You know that the lighthouse is 70 ft tall. How far from the lighthouse is the rowboat? Round your answer to the nearest foot. Define: Let x = the distance from the boat to the lighthouse. Relate: You know the angle of elevation and the opposite side. You are trying to find the adjacent side. Use the tangent.

  8. opposite leg adjacent leg Write: tan A = tan 70° = Substitute for the angle and the sides. x(tan 70°) = 70 Multiply each side by x. x = Divide each side by tan 70°. 70 tan 70 x 25.4779164 Use a calculator. x 25 Round to the nearest unit. 70 X Example 4: Finding the Measures of an Angle The rowboat is about 25 feet from the lighthouse.

  9. Draw a diagram. Example 5: Using an Angle of Elevation or Depression A pilot is flying a plane 15,000 ft above the ground. The pilot begins a 3° descent to an airport runway. How far is the airplane from the start of the runway (in ground distance)? Define: Let x = the ground distance from the start of the runway. Relate: You know the angle of depression and the opposite side. You are trying to find the adjacent side. Use the tangent.

  10. opposite leg adjacent leg Write: tan A = tan 3° = Substitute for the angle and the sides. 15,000 x x(tan 3°) = 15,000 Multiply each side by x. x = Divide each side by tan 3°. 15,000 tan 3 x 286217.05 Use a calculator. x 290,000 Round to the nearest 10,000 feet. Example 5: Using an Angle of Elevation or Depression The airplane is about 290,000 feet (or about 55 miles) from the start of the runway.

  11. Assignment: pg. 649-650 8-35 Left

More Related