Question

a 10-ft vertical post casts a 20-in shadow at the same time a nearby cell phone tower casts a 125-ft shadow. how tall is the cell phone tower?

Answer 1

750 ft

Explanation:

the 2 situations are similar ( both right triangles ) with corresponding sides being in proportion.

let h be the height of the cell phone tower

We require the dimensions to be the same, using the conversion

1 foot = 12 inches , then

10 ft = 10 × 12 = 120 in

125 ft = 125 × 12 = 1500 in

then we obtain

`(h)/(1500)` =
`(120)/(20)` = 6 ( multiply both sides by 1500 to clear the fraction )

h = 1500 × 6 = 9000 in ( divide by 12 to convert to ft )

h = 9000 in ÷ 12 = 750 ft

that is the cell phone tower is 750 ft tall.