A 5-foot tall girl stands 15 feet from a statue. She must look at an angle of 60 degrees to see the top of the statue. Approximately how tall is the statue?
To find the approximate height of the statue, we can use trigonometry.
First, let's assign variables to the given information:
- The height of the girl is 5 feet.
- The distance between the girl and the statue is 15 feet.
- The angle at which the girl must look to see the top of the statue is 60 degrees.
We can create a right triangle by considering the girl's line of sight as the hypotenuse, the height of the girl as the side opposite to the angle, and the distance between the girl and the statue as the side adjacent to the angle.
Using the tangent function, we can write:
tan(60 degrees) = opposite/adjacent
Plugging in the known values, we have:
tan(60 degrees) = 5 feet/hypotenuse
To find the height of the statue (hypotenuse), we rearrange the equation:
hypotenuse = 5 feet / tan(60 degrees)
Calculating the value, we have:
hypotenuse = 5 feet / tan(60 degrees) ≈ 5 feet / 1.732 ≈ 2.89 feet
Therefore, the approximate height of the statue is 2.89 feet.
tan60 = Y/15,
Y = 15tan60 = 8.66 Ft.
h = 5 + 8.66 = 13.66 Ft. = Height of
statue.