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Question

From the top of a cliff 50m high, the angles of depression of the top and bottom of a tower are observed to be 30° and 45°.

The height of tower is


A

50m

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B

503m

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C

50(31)m

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D

50(133)m

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Solution

The correct option is D

50(133)m


Explanation for the correct option:

Step 1. Draw the figure according to the question:

From the figure, we get

BD=50m

AE=Height of the tower (h)

DEC=30°

DAB=45°

BA=CE

=x m

Step 2. From the right-angled DEC,

tan30°=DCCE

=[50h]x

13=[50h]x

x=3(50h) — (i)

Step 3. From the right-angled BAD,

tan45°=DBBA

1=50x

x=50— (ii)

Step 4. From (i) and (ii), we get

50=(50h)3

50503=h3

h=[50(31)]3

h=50(133)m

Hence, Option ‘D’ is Correct.


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