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Discovery Activity Examine the figure below. What can you say about BCD,  GCE, and ACF?

A. G. B. C. D. E. F. Discovery Activity Examine the figure below. What can you say about BCD,  GCE, and ACF?. They are all right triangles that share a common angle at C. They are similar triangles.

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Discovery Activity Examine the figure below. What can you say about BCD,  GCE, and ACF?

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  1. A G B C D E F Discovery Activity Examine the figure below. What can you say about BCD,  GCE, and ACF? They are all right triangles that share a common angle at C. They are similar triangles.

  2. On graph paper, make a nest of three right triangles like the one below. Are your three triangles similar? A G B 10 8 6 12 C D E F 16 20 Measure the lengths of each leg on each triangle.

  3. Find the ratio between the leg opposite to angle C and the leg adjacent to angle C of each triangle. A G B 10 8 6 12 C D E F 16 20 What can you say about this ratio? This ratio is called the tangent ratio.

  4. B C A Notes (flipbook): For any similar right ∆s, the ratio of the leg opposite an  to the leg adjacent to the  is always the same number. This ratio is called the tangent ratio. Given a right : This only applies to the acute angles, never the right angle.

  5. B C A Examples 3 5 1. Given the right ,find tan A as a ratio (fraction). 4 Find tan B as a ratio. It depends on which angle you’re looking from. Often these ratios are written as a decimal value, rounded to 4 decimal places. 2. Given the right ,find tan A and tan B as a decimal.

  6. Since for a given angle measure the tangent ratio is always the same, you can use a chart or your calculator to tell values of tangent if you know the angle measure. Round to 4 decimals. 3. tan 15 _________ 4. tan 89 _________ 5. tan 30 _________ 6. tan 60 _________ Make sure your calculator is in “degree” mode FIRST! 0.2679 57.2900 0.5774 1.7321

  7. X 24 20 You can use the tangent ratio to solve for a missing side of a triangle. 7. Angle measure = 24 Opposite side = x Adjacent side = 20 Multiply each side by 20 to get x by itself. Use the calculator to evaluate (round to the nearest tenth). The length of side x is 8.9 units.

  8. 10 35 x Use your calculator to solve for a missing side of a triangle. 8. Angle measure is 35 Opposite side = 10 Adjacent side = x Multiply each side by x. Then divide by tan35 to get x by itself. Use the calculator to evaluate. Round to the nearest tenth. The length of side x is 14.3 units.

  9. The other two trig ratios work exactly the same way. For any similar right ∆s, the ratio of the leg opposite an  to the hypotenuse of the  is always the same number. This ratio is called the sine ratio. Given a right Δ: B A C

  10. B C A Examples 5 3 9. Given the right ,find sin A as a ratio (fraction). 4 Find sin B as a ratio. 10. Given the right ,find sin A as a decimal.

  11. Make sure your calculator is in “degree” mode FIRST! Use a chart or your calculator to tell values of sine if you know the angle measure. Round to 4 decimals. 11. sin 15 _________ 12. sin 89 _________ 0.2588 0.9998

  12. y 13 55° Solve for the missing side of the triangle. 13. Angle measure = 55 Opposite side = y Hypotenuse = 13 Multiply each side by 13 to get y by itself. Use the calculator to evaluate (round to the nearest tenth). The length of side y is 10.6 units.

  13. For any similar right ∆s, the ratio of the leg adjacent to an  to the hypotenuse of the  is always the same number. This ratio is called the cosine ratio. Given a right Δ: B A C

  14. B C A Examples 5 3 14. Given the right ,find cos A as a ratio (fraction). 4 15. Given the right ,find cos A as a decimal.

  15. Make sure your calculator is in “degree” mode FIRST! Use a chart or your calculator to tell values of cosine if you know the angle measure. Round to 4 decimals. 16. cos 15 _________ 17. cos 89 _________ 0.9659 0.0175

  16. 7 40° y Use your calculator to solve for a missing side of a triangle. 18. Angle measure is 40 Adjacent side = 7 Hypotenuse = y Multiply each side by y. Then divide by cos40 to get y by itself. Use the calculator to evaluate. Round to the nearest tenth. The length of side y is 9.1 units.

  17. If you know one of the trig ratios, you can use inverse functions to discover the angle measure. Use your calculator to find the missing angle measure. Round to the nearest degree. 19. Divide to get the decimal value. The inverse tangent function gets y by itself. Use the calculator (2nd TAN) to the angle measure. The measure of angle y = 23°.

  18. If you know one of the trig ratios, you can use inverse functions to discover the angle measure. 15 y 17 Use your calculator to find the missing angle measure. Round to the nearest degree. 20. Angle measure = y Adjacent side = 15 Hypotenuse = 17 Divide to get the decimal value. The inverse cosine function gets y by itself. Use the calculator (2nd COS) to the angle measure. The measure of angle y = 28°.

  19. in pp. over yp. os dj. over SOHCAHTOA yp. an pp. over dj.

  20. ome ld obo aught nother SOHCAHTOA obo aking ur pples

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