How tall is the flagpole?

Question

On a sunny day Jason sees that the shadow of a flagpole is about four times as long as his own shadow. If Jason is about 5.5 feet tall, about how tall is the flagpole?

Answer 1

Jason's height = 5.5ft

 

 

                                                                             Sun

                                                                               |

                                       Flagpole                             |

                                         |                                     |

              Jason                   |                                     |

                |                        |                                     |

θ________|_____________|_ _ _ _ _ _ _           _ _ _|

Jason's           

Shadow  >|

 

|<-----Flagpole's shadow-->|

 

 

In the above figure, the sun cast's shadows at the same angle, since it is in the same position in the sky. 

 

tanθ = opposite/adjacent = Jason's height/Jason't shadow  =  Flagpole's height/Flagpole's shadow

 

Let us assume Jason's shadow length is x . We know the flagpole's shadow length is 4 time that, i.e. 4x

 

Substituting these in the above equation

 

5.5ft / x  = flagpole's height / 4x

 

Solving for this, we get

 

flagpole's height = 5.5 * 4x / x  = 22 ft