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The angular depression of the top and the foot of a tower as s

Question

The angular depression of the top and the foot of a tower as seen from the top of a second tower which is $150 m$ high and standing on the same level as the first are $α$ and $β$ respectively. If $tan α = \frac{4}{3}$ and $tan β = \frac{5}{2}$ , the distance between their tops is:

100 m

120 m

110 m

130 m

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Samuel Discussed

The angular depression of the top and the foot of a tower as seen from the top of a second tower which is

150 m

high and standing on the same level as the first are

α

and

β

respectively. If

tan α = \frac{4}{3}

and

tan β = \frac{5}{2}

, the distance between their tops is:

8 mins ago

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Text solutionVerified

AB- 1st tower.

CD- 2nd tower.

Here given that CD

= 150 m

BE = C D = 150 m

From

△ BCE

tan β = \frac{BE}{CE}

or,

\frac{5}{2} = \frac{150}{CE}

or,

CE = 150 \times \frac{2}{5} = 60

tan α = \frac{4}{3}

sec α = 1 + \frac{16}{9} = \frac{25}{9} = \frac{5}{3}

[only positive value taken].

cos α = \frac{3}{5}

cos α = \frac{CE}{A C}

or,

\frac{60}{A C} = \frac{3}{5}

or,

A C = \frac{5}{3} \times 60 = 100

∴

Distance between their tops

= 100 m

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Question Text	The angular depression of the top and the foot of a tower as seen from the top of a second tower which is $150 m$ high and standing on the same level as the first are $α$ and $β$ respectively. If $tan α = \frac{4}{3}$ and $tan β = \frac{5}{2}$ , the distance between their tops is:
Answer Type	Text solution:1
Upvotes	150