# A pole that is 32 m tall casts a shadow that is 1.54 m long. At the same time, a nearby building...

## Question:

A pole that is 32 m tall casts a shadow that is 1.54 m long. At the same time, a nearby building casts a shadow that is 38.75 m long.

How tall is the building?

## Proportions:

Aristarchus, Hipparchus and Eratosthenes all used proportions, geometry and trigonometry in order to make the first recorded measurements of the distance of the earth from the sun, distance of the earth to the moon and the circumference of the earth.

The pole is 32 m high casts a 1.54-m long shadow. The nearby building has a 38.75-m long shadow, in order to get the height of the building, use the information given to make the ratios needed to form the proportion for the solution:

{eq}\begin{align} \rm \dfrac{x \ height \ of \ building}{ 38.75 \ meter \ shadow} &= \rm \dfrac{ 32\ height \ of \ pole}{ 1.54 \ meter \ shadow} \\ \dfrac x {38.75} &= \dfrac{32}{1.54} \\ x &= \dfrac{(32)(38.75)}{1.54} \\ x &= \dfrac {1,240}{1.54} \\ x &\approx 805.2 \end{align} {/eq}

The building is around {eq}\rm 805.2 \ meters {/eq} high.