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Q.

The Qutub Minar casts a shadow $150 m$ long, at the same time the Vikas Minar casts a shadow $120 m$ long on the ground. If the height of the Vikas Minar is $80 m$ , find the height of the Qutub Minar.

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a

180 m

b

100 m

c

150 m

d

120 m

answer is B.

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Detailed Solution

Given,
Height of the Vikas Minar = 80 m.
Shadow of Vikas Minar =120 m.
Since both the Qutub Minar and the Vikas Minar cast the shadow at the same time, the angle of elevation is same for both so far as the shadow cast by the sun is concerned.
Shadow of Qutub Minar = 150 m.
Let the height of Qutub Minar be h and the common angle of elevation be

α .

Consider the figure,
seo images

seo images

According to the figure,
⇒

\frac{Perpendicular}{Base} = tanα

∴ tanα = \frac{80}{120} = \frac{2}{3} (1)

(for Vikas minar)
For Qutub minar,
⇒

\frac{Perpendicular}{Base} = tanα

⇒

\frac{h}{150} = \frac{2}{3}

[using eq. (1)]
⇒

h = \frac{2}{3} \times 150

⇒h

= 100 m

Therefore, the height of the Qutub Minar is 100 m.
Hence, the correct option is 2.

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The Qutub Minar casts a shadow 150 m long, at the same time the Vikas Minar casts a shadow 120 m long on the ground. If the height of the Vikas Minar is 80 m, find the height of the Qutub Minar.