Question

Marcos is standing on a street in new york city looking at the top of the empire state building with a 29° angle of observation. He is standing 2 city blocks away from the building. If a city block is one fourth of a mile long how tall is the empire state building? Show all work.

If Marcos is 6feet tap how many marcoses would it take standing on top of each other to reach the top of the building?(hint: 1mile=5280 feet

Answer 1

1) We can calculate the height (which we will call "h") of The Empire State Building, by following the proccedure below:

Tan(α)=Opposite leg/Adjacent leg

α=29°
Opposite leg=H
Adjacent leg=1/4 mile

1 mile is 5280 feet, then:

Adjacent leg=(5280 feet)/4=1320 feet

Now, lets substitute these values into Tan(α)=Opposite leg/Adjacent leg:

Tan(α)=Opposite leg/Adjacent leg
Tan(29°)=h/1320
h=1320xTan(29°)
h=731.68 feet

How tall is The Empire State Building?

The answer is: 731.68 feet

2) The height of Marcos is 6 feet, so, if we want to calculate how many Marcoses would it take standing on top of each other to reach the top of The Empire State Building, we must divide the height of the building by the height of Marcos:

731.68 feet/6 feet= 122

Therefore, the answer is: 122 Marcoses