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Waec Bearing Question And Step By Step Solution by originalKsp(m): 8:39am On Apr 11, 2017 |
In a previous post, I introduced bearing and distances. Now, let's solve some bearing and distances questions. The following are the steps we will take in solving the problems: * Sketch the bearing * Sketch out a triangle * Apply the sine or cosine rule (or both). Example 3: Three towns, A, B and C are situated so that |AB| = 60km and |AC| = 100km. The bearing of B from A is 060degree and the bearing of C from A is 290degree. Calculate: a) the distance |BC|, b) the bearing of B from C ********************************** Solution ********************************** a) The distance |BC| From the question, we notice that the two bearings provided are from A, so it will be wise to start the sketch from point A, below is a sketch of B from A: Then of C from A, [ Notice that the lenght of the lines in the sketch reflects thats 100km is 'longer' that 60km ] At point A, the remaining unknown angle is given by 360degree - 290degree = 70degree. So the sketch becomes The triangle ABC is then given by Using the cosine rule to find the length a; a^2 = b^2 + c^2 - 2bcCosA a^2 = 100^2 + 60^2 - 2(60 X 100)Cos 130 a^2 = 10000 + 3600 - 12000Cos 130 From a calculator or tables of values, cos 130 = - 0.6428,then: a^2 = 13600 - 12000 X -0.6428 a^2 = 13600 + 7713.6 a^2 = 21313.6 a = √21313.6 a = 145.99 a = 146 km ( coverted to 1 decimal places ) Therefore, the distance |BC| = 146 km b) The bearing of B from C As shown in the diagram above, the bearing of B from C is given by 0xdegree in three figure bearings. To get the value of x, we will first find the value of the internal angle C in the triangle by using the sine rule. c/sin C= a/sin A Making sinC the subject of the formular gives; sin C = (c X sin A)/a sin C = (60 X Sin 130)/146 sin C = (60 X 0.7660)/146 sin C = 45.96/146 sin C = 0.3148 We will find the 'arc sin' of 0.3148 C = sin^{-1}0.3148 C = 18.35degree Remember the angle C we just found the value, is not the bearing of B from C, it is the internal angle of the triangle at C, see the sketch below: From the diagram above, we see that; x = 180 - (70 + 18.25) = 91.65degree x = 91.7degree. Whablamo! The bearing of B from C is 091.7 degree. Happy math. See full post here http://samimath.com/bearing-distance-explained-examples/ cc Richiez olawalebabs Fynestboi *singing* Help me call lala o - LALA lalasticlala - LALA lalasticlala - LALA Oya Help me call lala o - LALA 1 Like |
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