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A ladder 20 ft. long reaches a point 20 ft. below the top of a

Question

A ladder $20 f t$ . long reaches a point $20 f t$ . below the top of a flag. The angle of elevation of the top of the flag at the foot of the ladder is $6 0^{o}$ . Find the height of the flag.

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A ladder

20 f t

. long reaches a point

20 f t

. below the top of a flag. The angle of elevation of the top of the flag at the foot of the ladder is

6 0^{o}

. Find the height of the flag.

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Text solutionVerified

PB = l a dd er = BC = 20

given.
Also

∠ CP A = 6 0^{o} ∴ ∠ A CP = 3 0^{o}

∴ ∠ BCP = ∠ BPC = 3 0^{o}

△ A BC

is isosceles.

∴ ∠ BP A = 6 0^{o} - 3 0^{o} = 3 0^{o}

∴ A B = 30 sin 3 0^{o} = 20. \frac{1}{2} = 10

Hence the height of flag staff

= A B + BC = 10 + 20 = 30 f t .

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Question Text	A ladder $20 f t$ . long reaches a point $20 f t$ . below the top of a flag. The angle of elevation of the top of the flag at the foot of the ladder is $6 0^{o}$ . Find the height of the flag.
Answer Type	Text solution:1
Upvotes	151