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Calculating the Angle of Depression Using the Law of Sines in Flight Scenarios

This guide explains how to calculate the angle of depression from a small plane flying at 2000 ft when the horizontal distance to the runway is 2 miles. Utilizing the Law of Sines, the pilot can determine the angle θ, establishing a crucial component for safe landings. The document includes key formulas, examples, and practice problems to reinforce understanding. Topics covered include angle measures, triangle properties, and methods for solving for unknown sides or angles. Ideal for students and aviation enthusiasts mastering trigonometry applications in flight.

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Calculating the Angle of Depression Using the Law of Sines in Flight Scenarios

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  1. Warm_Up 5 1. The pilot of a small plane is flying at an altitude of 2000 ft. The pilot plans to start the final descent toward a runway when the horizontal distance between the plane and the runway is 2 mi. To the nearest degree, what will be the angle of depression θ from the plane to the runway at this point? 2. cos θ = 0.3, for 3π/2 < θ < 2π 13.5 Law of Sines

  2. Law of Sines Section 13.5 13.5 Law of Sines

  3. Use of Law of Sines • Two angle measures and any side length–angle-angle-side (AAS) or angle-side-angle (ASA) information • Two side lengths and the measure of an angle that is not between them–side-side-angle (SSA) information • Allows for triangles to find the missing side or angle • Law of Cosines are primarily used for SSS and SAS triangles 13.5 Law of Sines

  4. Equation • Put the equation as a proportion • Cross Multiply • Solve for the missing angle or side • Side always associates itself with OPPOSITE • Triangle has 180 degrees • Can’t use SOHCAHTOA because there is not a 90 degree angle Note: Letters A, B, C are not always going to be used as ‘A,’ ‘B,’ or ‘C’ 13.5 Law of Sines

  5. sin F sin D = d f sin 28° sin 33° = d 15 15 sin 33° d = sin 28° Example 1 Solve for d. Law of Sines. Substitute. d sin 28° = 15 sin 33° Cross multiply. Solve for the unknown side. d ≈ 17.4017 13.5 Law of Sines

  6. r Q Your Turn Determine q and r. 13.5 Law of Sines

  7. C C b 20 a 50 A B B c c Example 2 Determine the number of triangular banners that can be formed using the measurements a = 50, b = 20, and mA = 28°. Then solve for mB, mC, and side C. Round to the nearest tenth. 13.5 Law of Sines

  8. C 20 50 B c Example 2 Determine the number of triangular banners that can be formed using the measurements a = 50, b = 20, and mA = 28°. Then solve for mB, mC, and side C. Round to the nearest tenth. Law of Sines Substitute. Solve for sin B. C = 141.2°, c = 66.7 13.5 Law of Sines

  9. Your Turn Determine the number of triangular quilt pieces that can be formed by using the measurements a = 14 cm, b = 20 cm, and A = 39°. Solve for the missing sides. c1 21.7 cm; mB1≈ 64.0°; mC1≈ 77.0°; 13.5 Law of Sines

  10. Example 3 Given the points of (5, 3), determine the angle measure. 3 5 13.5 Law of Sines

  11. Your Turn Given the points of (–4, 3), determine the angle measure. 13.5 Law of Sines

  12. Page 962 13.5 Law of Sines

  13. Review Pg 978 39-47, 49, 51, 57-61 13.5 Law of Sines

  14. Assignment Page 962 5-9 odd, 17, 19, 24, 29 13.5 Law of Sines

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