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A building casts a shadow 30 m long. At the same time, the shadow cast by a 41-cm tall pole is 72 cm long. Find the height of the building.

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In this question, it is given that

A building casts a shadow 30 m long. At the same time, the shadow cast by a 41-cm tall pole is 72 cm long.

Let the height of the building be x m.

Now we set the ratio, which is

[tex] \frac{x}{3000}= \frac{41}{72}   [/tex]

Cross multiplication

[tex] 72x = 3000*41 \\ 72x = 123000 [/tex]

Dividing both sides by 72

[tex] x = \frac{123000}{72} = 1708.33 cm= 17 m [/tex]

Answer:

The height of the building is 17.08 m.

Step-by-step explanation:

Let the height of the building be h.

The building casts a shadow 30 m long. So, the ratio of object and its shadow is

[tex]r_1=\frac{x}{30}[/tex]

At the same time the shadow cast by a 41-cm tall pole is 72 cm long. So, the ratio of object and its shadow is

[tex]r_2=\frac{41}{72}[/tex]

The ratio of object and its shadow is same at a point of time.

[tex]r_1=r_2[/tex]

[tex]\frac{x}{30}=\frac{41}{72}[/tex]

On cross multiplication we get

[tex]72x=30\times 41[/tex]

[tex]72x=1230[/tex]

Divide both sides by 72.

[tex]x=\frac{1230}{72}[/tex]

[tex]x=17.0833\approx 17.08[/tex]

Therefore the height of the building is 17.08 m.

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