Bearings And Distances

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 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

Objectives

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

Theory

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.