Sine Rule and Cosine Rule Bearings Problems Sine Rule and Cosine Rule

Bearings Problems A set of problems on bearings, which need the sine rule and the cosine rule to solve them. Q1. The bearings and distances of two ships A and B from a port P are A [036º,144km] and B [114º,97km]. How far apart are the ships?

Bearings Problems Q2. A ship leaves port and sails 93km A set of problems on bearings, which need the sine rule and the cosine rule to solve them. Q2. A ship leaves port and sails 93km on a bearing 054º. It then turns and sails 108km on a bearing 110º. How far is the ship from the port?

Q3. Two radar stations Alpha and Beta pick up Bearings Problems A set of problems on bearings, which need the sine rule and the cosine rule to solve them. Q3. Two radar stations Alpha and Beta pick up signals from an incoming aircraft. Alpha is 40km east of Beta and picks up the signals on a bearing of 300º from Alpha. Beta picks up the signals on a bearing 070º. How far is the aero plane from Alpha?

Q4. An aero plane BA1445 is 200km from an Bearings Problems A set of problems on bearings, which need the sine rule and the cosine rule to solve them. Q4. An aero plane BA1445 is 200km from an airport on a bearing 208º, while a second aero plane Vir6334 is 170km from the same airport on a bearing 094º. How far apart are the aero planes?

Q5. The bearings and distances of two oilrigs from Aberdeen Bearings Problems A set of problems on bearings, which need the sine rule and the cosine rule to solve them. Q5. The bearings and distances of two oilrigs from Aberdeen are Oilrig1 [028º, 116km] and Oilrig2 [081º, 104km]. How far apart are the oilrigs?

Q6. An aero plane leaves Heathrow Bearings Problems A set of problems on bearings, which need the sine rule and the cosine rule to solve them. Q6. An aero plane leaves Heathrow and flies 400km on a bearing 160º. It then turns and flies 280km on a bearing of 100º. How far is it from the airport?

Q7. The bearings and distances of three oil rigs from a port are Bearings Problems Q7. The bearings and distances of three oil rigs from a port are Oilrig1 [047º,210km] Oilrig2 [110º,170km] Oilrig3 [180º,100km] A supply ship leaves port and visits the three oilrigs one after the other and then returns to port. Find the total distance traveled by the supply ship.

Solutions Question Solution 1 156.0km 2 Angle in triangle = 124°; Distance = 177.6km. 3 Use the sine rule; angles in triangle are 20°, 30° and 130°. Distance = 17.9km. 4 Angle in triangle = 114°; Distance = 310.7km. 5 Angle in triangle = 53°; Distance = 98.7km. 6 Angle in triangle = 120°; Distance = 591.9km. 7 Use the cosine rule twice to get 201.5km and 165.1km. Total = 676.6km