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Geom. B: Bellwork Sheet # 7

This instructional guide focuses on solving problems involving tangent ratios in trigonometry. Students will learn to find the values of unknown variables using the math concepts of tangent functions and their inverses. The exercises emphasize changing the calculator to degree mode for accurate results. Problems are designed to help students find lengths and angles, both by cross-multiplying and using inverse tangent calculations. Get ready to tackle trigonometric equations and enhance your understanding of geometric relationships!

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Geom. B: Bellwork Sheet # 7

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  1. X 12 Geom. B: Bellwork Sheet # 7 Solve for x. 9.4213 =

  2. 9-1 The Tangent Ratio

  3. B c a C b A tan A =opposite side adjacent side tan A = a b

  4. B EX. Write the tangent ratio for A and B. tan A = tan B= √65 4 C A 7

  5. Before starting this problem change your calculator mode to degrees EX 2. Find the value of w to the nearest tenth tan = 3.9 ≈ w CROSS MULTIPLY w 6 28° w 1 (6)tan28°=w 28° 6

  6. Before starting this problem change your calculator mode to degrees OYO. Find the value of w to the nearest tenth tan = 12.4 ≈ w CROSS MULTIPLY w 9 54° w 1 (9)tan54°=w 9 54°

  7. Before starting this problem change your calculator mode to degrees EX 3. Find the value of w to the nearest tenth tan = w ≈ 5.1 CROSS MULTIPLY 67° 12 w 12 1 tan67°(w)= 12 tan67° tan67° 67° w

  8. Before starting this problem change your calculator mode to degrees OYO. Find the value of w to the nearest tenth tan = w ≈ 9 CROSS MULTIPLY 48° 10 w 10 1 tan48°(w)= 10 tan48° tan48° w 48°

  9. EX. 4 Using the inverse of tangent Find m X to the nearest degree. tan X = = m X = tan-1(1.5) m X ≈ 56° N 12 8 1.5 12 R X 8

  10. OYO….Using the inverse of tangent Find m N to the nearest degree. tan N = = m N = tan-1(0.875) m N ≈ 41° N 14 16 1.5 16 R X 14

  11. Geometry B Bellwork 2)Find the value of w to the nearest tenth tan = 7.8 ≈ w CROSS MULTIPLY w 13 31° w 1 (13)tan31°=w 31° 13

  12. Geometry B Bellwork 3) Using the inverse of tangent Find m N to the nearest degree. tan N = = m N = tan-1(0.6) m N ≈ 31° N 18 30 1.5 30 R X 18

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