**BEARING 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 N45^{0}E, S60^{0}W

## More examples on bearing solved:

**General Evaluation**:

1)Find the corresponding bearing of the following: (a)N64^{0}W (b)064^{0} (c)S42^{0}E (d) 234^{0}

2)If the bearing of X from Y is N64^{0}W.Find the bearing of Y from X.

3)A boat sails 6km from a port X on a bearing of 065^{0} and thereafter 13km on a bearing of 136^{0}. 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 150^{0} 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**

**Objectives**

1. What is the equivalent of S70^{0}E in three digit notation? A. 110^{0} B. 070^{0} C.120^{0} D.100^{0}

2. If the bearing of P from R is 065^{0}, what is R from P? A. 230^{0 } B.245^{0} C. 120^{0} D 025^{0}

3. Express the true bearing 210^{0} as a compass bearing. A S30^{0}W B S60^{0}W C.N30^{0}W D.S60^{0}E

4. Town Q is on a bearing 210^{0} from town P, town R is on a bearing 150^{0} 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 315^{0}? A.065^{0} B. 015^{0} C. 045^{0 } D. 025^{0}

**Theory**

1. P, Q and R are points in the same horizontal plane. The bearing of Q from P is 150^{0} and the bearing of R from Q is 060^{0}. 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 38^{0} and from point B at the bottom of the building to be 65.4^{0}. 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.