# A person 6 feet tall casts a shadow 4 feet long. At the same time, a nearby tower casts a shadow 32 feet long. How many feet are in the height of the tower?

May 23, 2016

The height of the building is 48 feet

#### Explanation:

We can solve this by setting up a ratio comparing the height of the building to the height of the man and shadow of the building to the shadow of the man.

${h}_{b} =$ height of the building
${s}_{b} =$ shadow of the building
${h}_{m} =$ height of the man
${s}_{m} =$ shadow of the man

${h}_{b} / {s}_{b} = {h}_{m} / {s}_{m}$

 (?ft)/(32ft) = (6ft)/(4ft)

 (?ft)/cancel(32ft) xcancel(32 ft) = (6ft)/(4cancel(ft)) x 32cancel(ft)

 ?ft = 6ft x 8

${h}_{b} = 48 f t$