Further Mathematics Geometry & trigonometry Lesson 11

Transcription

1 Further Mathematics Geometry & trigonometry Lesson 11

2 Bearings Compass bearings indicate the direction to be followed. The main type of compass bearings in use is the Whole Circle or True bearing. These bearings use 0 T as orth and measure angles in a clockwise direction up to 360 T. The whole number of degrees is usually written as a three digit number, for example 008 T, 034 T, 267 T respectively. 360 T 000 T 270 T W 090 T E S 180 T 2

3 Bearings All bearings are in a horizontal plane. W E 70 S W E The bearing of B from A is 070 T S The bearing of A from B is 250 T True bearings differ by 180 when reading from each end of the same straight line. 3

4 Example 1 (i) A hiker walks 10 km from their camp to a large tree on a bearing of 235 T. How far south of their starting point will they now be? 10 km T 10 km 55 S cos 55 = S 10 Giving S = 10 cos 55 = 5.7 km 4

5 Example 1 (ii) A hiker walks 10 km from their camp to a large tree on a bearing of 235 T. How far south of their starting point will they now be? 10 km T 10 km 55 sin 55 = W W 10 Giving W = 10 sin 55 = 8.2 km VCE Further Mathematics Unit 3&4 We do our best to make these slides comprehensive and up- to- date, however there may be errors. 5

6 Example 1 (iii) A hiker walks 10 km from their camp to a large tree on a bearing of 235 T. Find the bearing for their return trip if the hiker heads directly back to their camp. 235 T 10 km Return bearing = 235 ± 180 = 415 OR 055 VCE Further Mathematics Unit 3&4 We do our best to make these slides comprehensive and up- to- date, however there may be errors. 6

7 Example 2(a) A yacht left harbour on a bearing of 040 T. After sailing 18 km to point A, the bearing was changed to 130 T and the yacht maintained this course for 14 km until it reached point B. Find the distance the yacht is from the harbor, to the nearest km. 40 H 18 km A km B In ΔHAB, use Cosine Rule to find HB? As HAB = 90, use Pythagoras Theorem. Hence : HB 2 = HB = = 22.8 km 23 km VCE Further Mathematics Unit 3&4 We do our best to make these slides comprehensive and up- to- date, however there may be errors. 7

8 Example 2(b) A yacht left harbour on a bearing of 040 T. After sailing 18 km to point A, the bearing was changed to 130 T and the yacht maintained this course for 14 km until it reached point B. Find the distance the yacht is from the harbor, to the nearest km. 40 H 18 km A km B To find HB, given HA, need to find AHB. In ΔHAB : 14 tan AHB = 18 AHB = tan = 37.9 so HB = = 77.9 The bearing of the yacht from the harbour is 078 T VCE Further Mathematics Unit 3&4 We do our best to make these slides comprehensive and up- to- date, however there may be errors. 8

9 Drill It Out (2009 Q3) The locations of three towns, Q, R and T, are shown in the diagram below. Town T is due south of town R. The angle TRQ is 48. The bearing of town R from town Q is A. 048 B. 132 C. 138 D. 228 E. 312 T R north 48 Q 9

10 Drill It Out A triangular course for a yacht race has three stages. Stage 1 is from the Start to Marker 1; a distance of 3.5 km on a bearing of 055. Stage 2 is from Marker 1 to Marker 2; a distance of 4.6 km on a bearing of 145. Stage 3 is from Marker 2 back to the Start. The distance travelled on Stage 3, in km, is closest to A. 4.9 B. 5.3 C. 5.8 D. 6.0 E. 7.7 (2012 Q8) 10

11 Drill It Out (2013 Q8) There are four telecommunication towers in a city. The towers are called Grey Tower, Black Tower, Silver Tower and White Tower. Grey Tower is 10 km due west of Black Tower. Silver Tower is 10 km from Grey Tower on a bearing of 300. White Tower is 10 km due north of Silver Tower. Correct to the nearest degree, the bearing of Black Tower from White Tower is : A. 051 B. 129 C. 141 D. 309 E

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