Pythagorean Theorem, The height of sueLo's 5th floor apartment window off the ground is 10 feet longer than the distance from the base of the apartment building to wall. She is concerned that the fire department's 50-foot ladder would not be able to reach her window in case of an emergency. (assume that the ladder must be positioned against the wall.
Let w = distance to wall
50^2 = w^2 + (w + 10)^2
Solve for w.
To determine whether the fire department's 50-foot ladder would be able to reach SueLo's window, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle formed by the height of the apartment window, the distance from the base of the apartment building to the wall, and the ladder. Let's call the distance from the base of the building to the wall "x" (in feet) and the height of SueLo's window "h" (in feet).
According to the problem, the height of the window is 10 feet longer than the distance from the base of the building to the wall. Therefore:
h = x + 10
Using the Pythagorean Theorem, we have:
h^2 + x^2 = 50^2
Now, we can substitute the value of h from the first equation into the second equation:
(x + 10)^2 + x^2 = 50^2
Expanding and simplifying the equation:
x^2 + 20x + 100 + x^2 = 2500
2x^2 + 20x + 100 - 2500 = 0
2x^2 + 20x - 2400 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Once we find the value of x, we can substitute it back into the equation h = x + 10 to find the height of the window.
By solving this equation, we can determine whether the ladder will be able to reach SueLo's window in case of an emergency.