he Statue of Liberty is approximately 305 feet tall. If the angle of elevation of a ship to the top of the statue is 22.9 degrees , how far, to the nearest foot, is the ship from the statue's base?

722 feet

Step-by-step explanation:

Tan (22.9) = 305/base

Base = 305/tan (22.9)

Base = 722.036124

To the nearest foot, 722 feet

is at a distance of 722 feet

Step-by-step explanation:

we have the angle that forms between the water and the imaginary line between the ship and the tip of the statue

we have the statue height that would be the opposite leg to our angle and we want to know the distance of the ship to the statue that would be the adjacent leg

we see that it has (angle, adjacent, opposite)

well to start we have to know the relationship between angles, legas and the hypotenuse

a: adjacent

o: opposite

h: hypotenuse

sin α = o/h

cos α = a/h

tan α = o/a

it's the tangent

tan α = o/a

we replace the values and solve

tan α = o/a

tan 22.9 = 305/a

a = 305/tan22.9

a = 305/0.4224

a = 722

is at a distance of 722 feet