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Trigonometric Ratios

Learn how to use trigonometric ratios, specifically the tangent ratio, to find missing side lengths and solve problems involving triangles. Includes examples and practice exercises.

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Trigonometric Ratios

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  1. Trigonometric Ratios How do you use trig ratios? M2 Unit 2: Day 4

  2. Using tangent tan70o = x. tan70o = opp. adj. 40. 40 ● tan 70o = x 109.9 x ANSWER x is about 110 . EXAMPLE 3 Remember…SOHCAHTOA Example 1 Find value of xin the triangle. Write ratio for tangent of 70o. Substitute. x Multiply each side by 40. 700 Use a calculator to simplify. 40

  3. Remember…SOHCAHTOA x tan32o = opp. adj. tan32o 11 = 11 = x x = xtan 32o 11 11 tan32o 0.6249 EXAMPLE 2 Example 2 Find the value of x. SOLUTION Use the tangent of an acute angle to find a leg length. Write ratio for tangent of 32o. Substitute. Multiply each side by x. Divide each side by tan 32o Use a calculator to find tan 32o X ≈ 17.6 Simplify

  4. Remember…SOHCAHTOA Example 3: Find the value of each variable. Round decimals to the nearest tenth. *Once you have 2 sides of a triangle, you can use the Pythagorean Theorem to find the missing third side.

  5. Example 4: Find the value of each variable. Round decimals to the nearest tenth.

  6. Example 5: Find the value of each variable. Round decimals to the nearest tenth.

  7. Example 6: Find the area of the triangle. Round decimals to the nearest tenth. We need to know the lengths of the sides! 45o It is a 45o45o90o triangle!

  8. Example 7: Find the area of the triangle. Write your answer in simplest radical form and find the decimal approximation to the nearest tenth. We need to know the altitude. a 4 x

  9. Example 8: Find the perimeter of the triangle. Round decimals to the nearest tenth. We need to use a trig ratio.

  10. Example 9: Find the perimeter of the triangle. Write your answer in simplest radical form. It’s a 30o60o90o triangle. 12 60o

  11. Example 10: Find the perimeter of the triangle. Round decimals to the nearest tenth. We need to use a trig ratio. 20o

  12. Homework: pg 159-160 #11-19 odds pg 168 #9-12 all MAKE SURE YOU SHOW YOUR WORK AND DRAW THE DIAGRAMS!

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