Question

The Big Ben clocktower in London is approximately 316 feet tall. Shana is standing nearby and notices that she casts a 4-foot shadow. If Shana is 5 feet tall, find the length of Big Ben's shadow?

Answer 1

The length of Big Ben shadow is 252.8 feet

Explanation:

The given parameters are;

The height of the Big Ben clocktower in London ≈ 316 feet tall

The length of the shadow Shana casts = 4-foot

The height of Shania = 5 feet

Therefore, we have, by similar triangles;

`(The \ length \ of \ the \ shadow \ Shana \ casts )/(The \ height \ of \ Shania) = (The \ length \ of \ the \ shadow \ The \ Big \ Ben \ casts)/(The \ height \ of \ the \ Big \ Ben \ clocktower)`Substituting the values, gives;

`(4 \ feet)/(5 \ feet) = (The \ length \ of \ the \ shadow \ The \ Big \ Ben \ casts)/(316 \ feet)`

`The \, length \, of \, the \, shadow \, The \, Big \, Ben \ clocktower \ casts = 316 \ feet * (4 \ feet)/(5 \ feet) = 252.8 \ feet`

The length of the shadow The Big Ben clocktower casts = The length of Big Ben shadow = 252.8 feet