BACCALAURÉAT GÉNÉRAL ET TECHNOLOGIQUE SESSION 2009 ÉPREUVE SPECIFIQUE MENTION « SECTION EUROPEENNE OU DE LANGUE ORIENTALE »
Académies de Paris, Créteil, Versailles Binôme : Anglais / Mathématiques Sujet n° 14 PLANE GEOMETRY The first part of this page is a summary that can be helpful to do the exercise. Bearings
north
A bearing is an angle, measured clockwise from the north direction. The bearing of B from A is 070 degrees (note 3 figures are always given) as shown in the diagram. Question: What is the bearing of A from B ?
north
B 70
A
Solving triangles In a right-angled triangle, trigonometric ratios and Pythagoras’ theorem can be used. Otherwise, triangles may be solved by using the following formulas : a b c = = called the sine rule; sin A sin B sin C a 2 = b 2 + c 2 − 2bc cos A called the cosine rule.
EXERCISE A ship leaves port P and sails 15 km to Q which is east of P. The journey from P to R takes 1 h 10 min. A second ship leaves P at the same time as the first ship and sails directly to R averaging 24 km/h. R is north of Q. The second ship then changes directions and sails directly east to S, which is 25 km from R. Calculate : (a) distance PR. (b) the bearing of R from S. (c) distance QR to the nearest km. (d) the bearing of S from Q. (e) the bearing of Q from S. (f) distance PS to the nearest km.
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