Question

A woman wants to measure the height of a nearby building she plays with a 6 foot pole in the shadow of the building so that the shadow of the pole is exactly covered by the shuttle of the building the total length of the buildings shadow is 170 feet in the polecats a shadow that is 3.5 foot long how tall is the building round your answer to the nearest foot

Answer 1

Let's put more details in the given figure to better understand the problem:

Since it appears that the two triangles formed are similar triangle, we can determine the height of the building by ratios and proportions,

We get,

`\text{ }\frac{\text{ h}}{\text{ 170}}\text{ = }\frac{\text{ 6}}{\text{ 3.5}}`
`\text{ h x 3.5 = 6 x 170}`
`\text{ 3.5h = 1,020}`
`\text{ }\frac{\text{3.5h}}{\text{ 3.5}}\text{ = }\frac{\text{1,020}}{\text{ 3.5}}`
`\text{ h = }291.42857142857\text{ }\approx\text{ 291 Feet}`

Therefore, the height of the building is approximat291 Feet.