Question

2. Let A, B and c be three towers. The bearing of B from A is 120° and angle BC is 68º. The distance from Tower A to Tower B is 145 m and the distance from Tower B to Tower C is 240 m. N A 120 145 m wer 58 B (1) Determine the value of angle X. (ii) Calculate the bearing of A from B. (iii) Calculate the bearing of C from B. (iv) Find, to the nearest metre, the distance AC. [3]

Answer 1

(i) The bearing of B from A and angle x are supplementary, then:

`\begin{gathered} 120\degree+x=180\degree \\ x=180\degree-120\degree \\ x=60\degree \end{gathered}`

(ii)

From the above diagram, the bearing angle of A from B is:

`120\degree+180\degree=300\degree`

(iii)

From the above diagram, the bearing angle of C from B is:

`180\degree+52\degree=232\degree`

(iv)

Applying the law of cosines with the sides AB = 145m and CB = 240 m, and the angle ABC = 68°, the distance AC is: