In this q what have we dine to PD in the last step. Is it rationalisation ?

In this q what have we dine to PD in the last step. Is it rationalisation ? : ne angles ofdepression ofthe top and the bottom Ofan 8 m from the top ofa multi-storeyed building are 300 and 450, respectively F' I ofthe multi-storeyed building and the distance between the two Solution : In Fig 9.9, PC denotes the multi- storyed building and AB denotes the 8 m tall building. We are interested to determine the height of the multi-storeyed building, i.e., PC and the distance between the two buildings, i.e., AC. Look at the figure carefully. Observe that PB is a transversal to the parallel lines PQ and BD. Therefore, Z QPB and Z PBD are alternate angles, and so are equal. so L 300. Similarly, Z PAC 450 In right PBD. we have solation : In Fig 9.10, A and B represent points on the bank on ite sides of the river, so that the width of the river. P is int on the bridge at a height a po of 3 m, i.e., DP 3m. We are ted to determine the width of the river, which is the length of the side AB Of the A APB. AB - AD DB In right A APO, Z A = 309. Fig. 9.10 A 3 Fig. 9.9 so, PD tan 300 3 — = tan 300 or BD - PDV'S In right PAC, we have pc = tan I AC PC PD + DC, therefore, PD + DC AC. DC AB 8m, we get PD 8 = BD pmfi (Why?) This gives 866+ l) 8 {4(vfi + l) + = and between the two buildings is also + vfi)m. of depressitl' Also, in right PBD, z B 450. so, PD-3 m. AB- BD+AD=3+3vfi -30 Therefore, the width of the river is 3 (6 + l)m. EXERCISE 9.1 l. A which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole. if the angle made by the rope with the ground level is 300 (see Fig. 9.11). tree breaks due to storm and the broken part bends so that the top of the tree touches the ground B making an angle 300 with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the

Dear Student,

Yes, in the last step rationalization is done,

PD = 83-1Rationalizing,PD = 83-1×3+13+1PD = 8×3+13-13+1Using a2-b2 = a-ba+bPD = 83+13-1PD = 83+12 = 43+1m.


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