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=101, find the height of the tower and the flag staff.

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=101​, find the height of the tower and the flag staff.

Filo · Accepted Answer

AB = y, tower, BC = x, flagstaff, AP = 9, AQ = 11. BC subtends equal angles

α

at P and Q s.t.

t an α = \frac{1}{10}

. 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 + 11 t an β

...(1)
and

x + y = 11 t an (α + β)

...(2)

A P = 9 = (x + y) t an β

...(3)

∴ 9 = 11 t an (α + β) t an β

,
from (2) and (3),
or

9 = 11 t an β (\frac{t an α + t an β}{1 - t an α t an β})

Put

t an α = \frac{1}{10}

.

∴ 9 [1 - (- \frac{1}{10}) t an β] = 11 t an β (\frac{1}{10} + t an β)

9 (10 - t an β) = 11 t an β (1 + 10 t an β)

.

110 t a n^{2} β + 20 t an β - 90 = 0

or

11 t a n^{2} β = 2 t an β - 9 = 0

(11 t an β - 9) (t an β + 1) = 0

∴ t an β = \frac{9}{11} (β a c u t e)

Hence from (1),

y = 11 t an β = 11. \frac{9}{11} = 9

From (3),

9 = (x + y) t an β = (x + 9) . \frac{9}{11}

.

∴ x + 9 = 11

or

x = 2

.

Question Text	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 $t an α = \frac{1}{10}$ , find the height of the tower and the flag staff.
Answer Type	Text solution:1
Upvotes	150

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 $t an α = \frac{1}{10}$ , find the height of the tower and the flag staff.

Text solutionVerified

Practice questions from similar books

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=101​, find the height of the tower and the flag staff.

Text solutionVerified

Practice questions from similar books

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 $t an α = \frac{1}{10}$ , find the height of the tower and the flag staff.