The firemen's ladder is 39 feet long (L).
The firemen set the base of the ladder 12 feet away from the building (d).
When the firemen lean the ladder against the building, the top of the ladder reaches the third floor window.
How high, in feet, is the third floor window from the ground (h)?
Round your answer to the nearest tenth (if necessary).
Do not include units (feet) in your answer.
Use the Pythagorean Theorem.
12^2 + b^2 = 39^2
To find the height of the third-floor window (h), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (L) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the ladder forms a right triangle with the ground and the height of the third-floor window. The length of the ladder (L) is the hypotenuse, and the distance from the base of the ladder to the building (d) is one of the other two sides.
Using the Pythagorean theorem, we have the equation:
L^2 = d^2 + h^2
Substituting the given values:
39^2 = 12^2 + h^2
Simplifying the equation:
1521 = 144 + h^2
Rearranging the equation:
h^2 = 1521 - 144
h^2 = 1377
To find h, we take the square root of both sides:
h = √1377
Using a scientific calculator or an online tool, we find:
h ≈ 37.1
Therefore, the height of the third-floor window is approximately 37.1 feet.