Answer :
Answer:
695 feet.
Step-by-step explanation:
Please find the attachment.
Let x represent distance between ship and base of statue.
We have been given that the Statue of Liberty is approximately 305 feet tall. The angle of elevation of a ship to the top of the statue is 23.7 degrees. We are asked to find the distance between ship and base of statue.
We can see that angle of elevation forms a right triangle with base of statue and ship.
Now, we will use tangent to solve for x as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(23.7^{\circ})=\frac{305}{x}[/tex]
[tex]x=\frac{305}{\text{tan}(23.7^{\circ})}[/tex]
[tex]x=\frac{305}{0.438969309852}[/tex]
[tex]x=694.80939\approx 695[/tex]
Therefore, the ship is approximately 695 feet away from the base of statue.
By using trigonometric relations, we will see that the distance is 694.81 ft.
How to find the distance between the ship and the statue?
Think of this as in a right triangle.
We know one angle of that triangle and the opposite cathetus to said angle, and we want to get the adjacent cathetus, which would be the distance between the ship and the statue.
We can use the trigonometric relation:
tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
- a = 23.7°
- opposite cathetus = 305ft
- adjacent cathetus = d.
We will have:
tan(23.7°) = 305ft/d
Solving this for d we get:
d = 305ft/tan(23.7°) = 694.81 ft
So the distance between the ship and the statue base is 694.81 ft
If you want to learn more about right triangles, you can read:
https://brainly.com/question/2217700