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