Question

A flagpole casts a shadow 3.5 meters long, Anita is standing near the pole. Her shadow is 0.75 meters long, Anita's height is 1.5 meters.How tall is the flagpole? Draw a diagram, label, and solve. Type your answer as a whole number or a decimal with no labels. EX5.2

Answer 1

The heights and the shadows are in the same ratio because the sun is shining from the same angle, so the triangles formed are similar.

Notice that Anita's height is twice as long as her shadow, so the height of the flagpole will be

`2\text{ x }3.5\text{ = 7m}`

We can also write a direct proportion:

`(x)/(3.5)\text{ = }(1.5)/(0.75)\text{ }\frac{\leftarrow\text{heights}}{\leftarrow shadows}`

solving for x, we get:

`x\text{ =}\frac{3.5\text{ x }1.5}{0.75}\text{ = 7m}`

then, we can conclude that the correct answer is:

`x\text{ = 7m}`