Question

A pole that is 3.1 m tall casts a shadow that is 1.1 m long. At the same time, a nearby building casts a shadow that is 37.25 m long. How tall is the building?Round your answer to the nearest meter.х5?

Answer 1

Let's determine the height of the building using ratios and proportions.

`\text{ }\frac{\text{ Height of Pole}}{\text{ Shadow length of Pole}}\text{ = }\frac{\text{ Height of Building}}{\text{ Shadow length of Building}}`
`\text{ }\frac{\text{ 3.1}}{\text{ 1.1}}\text{ = }\frac{\text{ h}}{\text{ 37.25}}`

Where,

h = height of the building

We get,

`\text{ }\frac{\text{ 3.1}}{\text{ 1.1}}\text{ = }\frac{\text{ h}}{\text{ 37.25}}`
`\text{ 3.1 x 37.25 = h x 1.1}`

`115.475=1.1h`

`(115.475)/(1.1)=(1.1h)/(1.1)`

`\begin{gathered} \text{ 104.97727272727 = h} \\ \text{ h = 104.97727272727} \end{gathered}`

`\text{ h }\approx\text{ 105 m}`

Therefore, the height of the building is approximately 105 m.