The lighthouse casts a shadow 28 meters long at 7 am.

Question

The lighthouse casts a shadow 28 meters long at 7 am. At the same time, the shadow of the lighthouse keeper, who is 1.75 meters tall, is 3.5 meters long. How tall is the lighthouse?    

Answer 1

Hi Tim,

For this problem we can set up a proportion between the shadow cast by the lighthouse and the height and shadow of the light house keeper.

1.7 5 m /3. 5 m = x/28

x is the height of the lighthouse..

Finish up the math to get the height.

I hope this helps

Answer 2

This can be set up as a proportion:

height lighthouse/length of the shadow = height of the keeper/length of the shadow

Let height of the lighthouse = x

x/28 = 1.75/3.5 To solve, cross multiply

3,5(x)=28(1.75) Simplify

3.5x=49 Divide both sides by 3.5

3.5x/3.5=49/3.5

x=14 m is the height of the lighthouse