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Two pillars of equal heights stand on either side of a road which is 150 m wide. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 45∘ and 30∘. Find their height and position of the point. |
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Answer» Step-by-step explanation: Let AB and CD be two PILLARS ,each of HEIGHT hmetres. Let P be a point on the road such that AP=xm. Then,CP =(150−x)m In triangle PAB , we have tan60o=APAB =3=xh =3x=h.....................1 In triangle PCD , we have tan30o=CPCD =31=150−xh =h3=150−x....................2 Eliminating h between eq. 1 and 2, we get 3x=150−x =x=37.5 Substituting x=37.5 in eq.1 we get , h=64.95 Thus the required point is at the distance of 37.5 m from the first pillar and 112.5 m from the SECOND pillar. The height of the pillars is 64.95 m  |
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