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A vertical tower 50 ft. high stands on a sloping ground. The f

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A vertical tower $50 f t$ . high stands on a sloping ground. The foot of the tower is at the same level as the middle point of a vertical flag pole. From the top of the tower the angle of depression of the top and the bottom of the pole are $1 5^{o}$ and $4 5^{o}$ respectively. Find the length of the pole.

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A vertical tower

50 f t

. high stands on a sloping ground. The foot of the tower is at the same level as the middle point of a vertical flag pole. From the top of the tower the angle of depression of the top and the bottom of the pole are

1 5^{o}

and

4 5^{o}

respectively. Find the length of the pole.

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Text solutionVerified

OC = 50

is the tower standing on a sloping ground

OB

B A = 2 h

is the flag pole whose mid-point

M

is in level with

O

.
The angles of depression of

A

and

B

as seen from

C

, the top of the tower, are

15^{o}

and

45^{o}

respectively.
Let

B D = x = OM = A E

50 - h = x tan 15, △ C A E

50 + h = x tan 45, △ CB D

Dividing in order to eliminate

x

, we get

\frac{50 + h}{50 - h} = \frac{tan 45}{tan 15}

Applying componendo and dividendo, we get

\frac{2 h}{100} = \frac{sin ( 45 - 15 )}{sin ( 45 + 15 )} = \frac{sin 30}{sin 60} = \frac{1}{3}

∴ 2 h = \frac{100}{3} = \frac{100 3}{3}

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Question Text	A vertical tower $50 f t$ . high stands on a sloping ground. The foot of the tower is at the same level as the middle point of a vertical flag pole. From the top of the tower the angle of depression of the top and the bottom of the pole are $1 5^{o}$ and $4 5^{o}$ respectively. Find the length of the pole.
Answer Type	Text solution:1
Upvotes	150

A vertical tower 50 ft. high stands on a sloping ground. The foot of the tower is at the same level as the middle point of a vertical flag pole. From the top of the tower the angle of depression of the top and the bottom of the pole are 15o and 45o respectively. Find the length of the pole.

Text solutionVerified

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