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MPM2D Unit #6 - Trigonometry Sine & Cosine Law Part B - Concept Determine whether you should use the sine law or the cosine law to solve each triangle. Sine Law or Cosine Law? Diagram 5.1 cm H 3.6 cm I 5.2 cm G a) K 70° 3.7 cm L 59° J b) N 5.0 cm 72° M 4.4 cm O c) Q 5.6 cm P 45° 4.8 cm R d) Reason MPM2D Date ______________ Sine Law and Cosine Law - Applications 1. A ship is sailing a course from A to B, past a lighthouse at C. The angles are <A= 45O and <B= 55O. If the distance from A to B is 6km, find AC and BC. (5 km, 4.3 km) A A B C C B 2. Chuck Wagon is building a cottage. The width of the cottage is 20m. On one side the angle of the roof is 25O and on the other side the angle is 70O. Find the lengths of the rafters (AB and AC). (18.9 m, 8.5 m) 20m 3. Sandy Beach is standing on the shore of a lake at C. He knows the distance CA is 3 km, CB is 2.5 km and the angle at C is 70O. Find the width of the lake, AB. (3.2 km) B A C 4. A hockey net is 2m wide. A player shoots from a point where the puck is 13m from one goal post and 12m from the other goal post. Within what angle must she make her shot to hit the net? (8O) 12m 13m ? 5. Two hunters, Frank and Buck, are hiding in a swamp. They are 100m apart. A duck lands in the water. The angles formed are shown. Find the distance between Buck and the Duck. (66.5m) 1 40O Frank 65O Buck 6. Ray Dar runs a radar station. From his station the bearing of a plane 100 km away, is N 40O E. Another plane is on a bearing of N 45O W and is 220 km away. Find the distance between the two planes. (233.6km) N 220 km 45 O O 40 100 km W E Station 7. Patty Cake and Jim Nasium are flying a kite. Patty is 200 m away from Jim who is holding the kite. Facing Jim, Patty finds the angle of elevation of the kite is 40O. If the kite string makes an angle of 85O with the ground, find the amount of string let out by Jim. (156.9m) Jim 40O 85O 200m Patty 8. Town A is 80km west of town B. From town A, the angle the elevation to a satellite is 45O and the angle of elevation from town B is 60O. Both towns are on the same side of the satellite. How far is the satellite from town B? (218km) 45O A 60O 80 km B 9. Two roads from the Quebec town of Deux Rues are at an angle of 15O. Yves Trough takes one road and walks at 5 km/h, while Dwain Pipe takes the other road and walks at 3 km/h. How far apart are Yves and Dwain after 2 hours? (4.5 km) Yves Dwain 15O 2 Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner Scanned by CamScanner