wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

A tower has flag staff at its top which subtends equal angles α at a points distance 9 yds and 11 yds from the foot of the tower. If tanα=110, find the height of the tower and the flag staff.

Open in App
Solution

AB = y, tower, BC = x, flagstaff, AP = 9, AQ = 11. BC subtends equal angles α at P and Q s.t. tanα=110. Hence the circle through C and B must also pass through P and Q as angles in the same segment are equal. From the figure it is clear that segment BP subtends equal angles say β at C and Q.
y+11tanβ ...(1)
and x+y=11tan(α+β) ...(2)
AP=9=(x+y)tanβ ...(3)
9=11tan(α+β)tanβ,
from (2) and (3),
or 9=11tanβ(tanα+tanβ1tanαtanβ)
Put tanα=110.
9[1(110)tanβ]=11tanβ(110+tanβ)
9(10tanβ)=11tanβ(1+10tanβ).
110tan2β+20tanβ90=0
or 11tan2β=2tanβ9=0
(11tanβ9)(tanβ+1)=0
tanβ=911(βacute)
Hence from (1),
y=11tanβ=11.911=9
From (3),
9=(x+y)tanβ=(x+9).911.
x+9=11 or x=2.
1085292_1007625_ans_059b955381bb467ab88375a728a4624e.JPG

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Transformations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon