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Warm Up Apr. 30 th

Warm Up Apr. 30 th. A 100-foot line is attached to a kite. When the kite has pulled the line taut, the angle of elevation to the kite is 50°. Find the height of the kite.

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Warm Up Apr. 30 th

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  1. Warm Up Apr. 30th • A 100-foot line is attached to a kite. When the kite has pulled the line taut, the angle of elevation to the kite is 50°. Find the height of the kite. • At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack on top of the building is 35° and the angle of elevation to the top is 53°. Find the height of just the smoke stack.

  2. Homework Questions??

  3. Solving Triangles Develop and understand the Law of Sines & Cosines. Use them to solve oblique triangles and applications.

  4. Get your bearings… Bearing measures the acute angle a path or line of sight makes with a fixed north-south or east-west line. For example: S 35 E or W 10 N

  5. Example • An airplane flying at 600 mph has a bearing of S 34 E. After flying 3 hours, how far south has the plane traveled from its departure?

  6. Oblique Triangles • Triangles without a right angle. • To solve any oblique triangle, you need to know at least ONE SIDE and any two other parts. • 2 angles, 1 side (ASA or AAS) • 2 sides, angle opposite one of them (SSA) • 3 sides (SSS) • 2 sides and the included angle (SAS)

  7. If you’re given 2 angles and 1 side (ASA or AAS) use the Law of Sines Law of Sines

  8. Example • Solve the triangle ABC: A = 35o, B = 100o, a = 8

  9. Applications • Tracking station B is located 110 miles east of station A. A forest fire is located at C, on a bearing N42°E of station A and N15°E of station B. How far is the forest fire from station A?

  10. B c a C A b If you are given • three sides (SSS) or • two sides and the included angle (SAS) then solve use Law of Cosines to start off.

  11. Application • Two planes leave the same airport at the same time. The first plane is traveling 500 mph bearing W 30ºN. The second plane is bearing N 27º W traveling at 600 mph. How far apart are the planes after 3 hours?

  12. Example • Solve the triangle DEF: d = 8.2, e = 3.7, f = 10.8

  13. You Try! • Solve each triangle: • ∆ABC: A = 10o, B = 60o, a = 4.5 • ∆PQR: p = 21, r = 15, q = 10 • ∆JKL: J = 59o, L = 47o, k = 100 • To approximate the length of a marsh, a surveyor walks 380 meters from point A to B, then turns 80° and walks 240 meters to point C. Approximate the length AC of the marsh. B 80° C A

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