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
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?
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?
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?
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?
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?
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