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A vertical tower stands on a declivity which is inclined at 15

Question

A vertical tower stands on a declivity which is inclined at $1 5^{o}$ to the horizon. From the foot of the tower a man ascends the declivity for $80$ feet and then finds that the tower subtends at angle of $3 0^{o}$ . The height of the tower is-

20 (6 - 2)

40 (6 - 2)

40 (6 + 2)

n o n e o f t h ese

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A vertical tower stands on a declivity which is inclined at

1 5^{o}

to the horizon. From the foot of the tower a man ascends the declivity for

80

feet and then finds that the tower subtends at angle of

3 0^{o}

. The height of the tower is-

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Text solutionVerified

From triangle ABC by sine formula

\frac{BC}{s in 7 5 ^{o}} = \frac{A B}{s in 3 0 ^{o}}

h = 80 \frac{s in 3 0 ^{o}}{s in ( 4 5 ^{o} + 3 0 ^{o} )} = \frac{40 \times 2 2}{[ ( 3 ) + 1 ]}

= \frac{40.2 2 ( 3 - 1 )}{3 - 1} = 402 (3 - 1) = 40 (6 - 2)

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Question Text	A vertical tower stands on a declivity which is inclined at $1 5^{o}$ to the horizon. From the foot of the tower a man ascends the declivity for $80$ feet and then finds that the tower subtends at angle of $3 0^{o}$ . The height of the tower is-
Answer Type	Text solution:1
Upvotes	150