Mathematics Notes

Bearings And Distances


Bearings can be defined as the angular relationships between two or more places. Bearings are specified in two ways:

Cardinal Points: It is specified in reference to the north and south. E.g N450E, S600W

More examples on bearing solved:

General   Evaluation:

1)Find  the  corresponding bearing  of the  following: (a)N640W  (b)0640  (c)S420E  (d) 2340

2)If  the bearing  of  X  from  Y  is  N640W.Find  the  bearing  of  Y   from  X.                                                                                                                                              

3)A boat sails 6km from a port X on a bearing of 0650 and thereafter 13km on a bearing of 1360. What is the distance and bearing of the boat from X.

4. Find the angle of elevation to the nearest degree of the top of a church tower 180m high from a point on the ground 75m from its foot.

Revision Questions

1 From a place 400m north of X, a student walks eastward to a place Y which is 800m from X. What is the bearing of X from Y

2 In a circle of radius 18cm, two radii form an angle of 1500 at the centre from point X and Y on the circumference. Find correct to three significant figure

(a) the length of the chord XY

(b) the length of the major arc

(c) the area of the minor segment

Reading Assignment

Essential Mathematics SSS2, pages 195-197, nos 1-10.

Weekend  Assignment


1. What is the equivalent of S700E in three digit notation?  A. 1100   B. 0700   C.1200   D.1000

2. If the bearing of P from R is 0650, what is R from P?  A. 2300     B.2450    C. 1200     D 0250

3. Express the true bearing 2100 as a compass bearing. A S300W  B S600W C.N300W   D.S600E

4. Town Q is on a bearing 2100 from town P, town R is on a bearing 1500 from town P and R is east of Q. The distance between R and P is 10km. Find the distance between R and Q.  A. 10km  B. 20km C.30km D. 40km

5. What is the bearing of M from N, if the bearing of N from M is 3150? A.0650  B. 0150   C. 0450   D. 0250


1. P, Q and R are points in the same horizontal plane. The bearing of Q from P is 1500 and the bearing of R from Q is 0600. If |PQ| = 5m and |QR| = 3m. Find the bearing of R from P correct to the nearest degree.

2.The angles of elevation of the top T, of a tower, 25m high are observed from point A at the top of a building to be 380 and from point B at the bottom of the building to be 65.40. If the tower and the building are on the same horizontal level, calculate (a) BT   (B) the height of the building. Give your answers correct to 3 s.f.

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