Question

A pole that is 3.3 m tall casts a shadow that is 1.4 m long. At the same time, a nearby building casts a shadow that is 47.5 m long. How tall is the building?

Round your answer to the nearest meter.

Answer 1

`112\:\mathrm{m}`

Explanation:

If you were to draw a diagram, you could form two similar triangles using the pole and the building (unsolvable otherwise). Since these triangles are similar, we can write the following proportion:

`(3.3)/(1.4)=(h)/(47.5)`, where
`h` is the height of the building.

Solving, we get:

`h=(47.5\cdot 3.3)/(1.4),\\h\approx \fbox{$112\:\mathrm{m}$}` (rounded to the nearest meter as requested in the problem).

I've drawn the figure below for reference: