**Question**

The diagram shows a field, ABCD, on horizontal ground.

BC = 192m, CD = 287.9m, BD = 168m and AD = 205.8m.

(a) (i) Calculate angle CBD and show that it rounds to 106.0°, correct to 1 decimal place.

(ii) The bearing of D from B is 038°.

Find the bearing of C from B.

………………………………………….

(iii) A is due east of B.

Calculate the bearing of D from A.

………………………………………….**(b) (i) Calculate the area of triangle BCD.****……………………………………..\( m^{2}\)****(ii) Tomas buys the triangular part of the field, BCD.****The cost is \($35 750\) per hectare.****Calculate the amount he pays.****Give your answer correct to the nearest \($100.\)****[1 hectare = \(10000m^{2}\)]****\($ …………………………………………\)**

**Answer/Explanation**

(a)(i) 106.01 to 106.02

(ii) 292.0 or 291.98 to 291.99

(iii) 310.0 or 310.03 to 310.04

(b)(i) 15 500 or 15 501 to 15 503. …

(ii) 55 400

*Question*

The diagram shows a triangular field, ABC, on horizontal ground.

**(a)** Olav runs from A to B at a constant speed of 4m/s and then from B to C at a constant speed of 3m/s.

He then runs at a constant speed from C to A.

His average speed for the whole journey is 3.6m/s.

Calculate his speed when he runs from C to A.

m/s [3]

**(b) Use the cosine rule to find angle BAC.**

**Angle BAC = [4]**

**(c)** The bearing of C from A is 210°.

**(i)** Find the bearing of B from A.[1]

**(ii)** Find the bearing of A from B.[2]

**(d)** D is the point on AC that is nearest to B.

Calculate the distance from D to A.

m [2]

**Answer/Explanation**

Ans:

**5(a)** 4.29 or 4.285 to 4.286

**5(b)** 82.8 or 82.81 to 82.82 using cosine rule

**5(c)(i)** 127.2 or 127.1 to 127.2 or 127

**5(c)(ii)** 307.2 or 307.1 to 307.2 or 307

**5(d)** 15 or 14.99 to 15.04

**Question**

**Question**

The diagram shows two ports, L and P, and a buoy, M.

The bearing of L from P is 201° and LP = 248km.

The bearing of M from P is 127°.

Angle PML = 42°.**(a) Use the sine rule to calculate LM.****LM = ………………………………….. km**

(b) A ship sails directly from L to P.

(i) Calculate the shortest distance from M to LP.

…………………………………… km

(ii) The ship leaves L at 2045 and travels at a speed of 40km/h.

Calculate the time the next day that the ship arrives at P.

………………………………………….

**Answer/Explanation**

(a) 356 or 356.2 to 356.3

(b)(i) 320 or 319.9 to 320.2…

(ii) 02 57 or 257 am