A 50 foot ladder is placed against a building so that it touches a point 40 feet above the ground. The distances ( in feet ) from the foot of the ladder to the building is
a. 10
b. 20
c. 30
d. 45
e. 60
please answer and explain
Pythagorean Theorem:
40^2 + b^2 = 50^2
1,600 + b^2 = 2,500
b^2 = 900
b = 30
I understand now, like a triangle
a^2 + b^2 = c^2
thank you
Yes!
You're welcome.
To find the distance from the foot of the ladder to the building, we can use the Pythagorean theorem, which 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, the ladder forms the hypotenuse of a right triangle, with one side being the height of the building (40 feet) and the other side being the distance we need to find.
Let's represent the unknown distance as x. Therefore, the Pythagorean theorem can be written as:
x^2 + 40^2 = 50^2
Simplifying the equation, we have:
x^2 + 1600 = 2500
Subtracting 1600 from both sides, we get:
x^2 = 900
Now, to find the value of x, we take the square root of both sides:
√(x^2) = √(900)
x = 30 or -30
Since distance cannot be negative, the answer is x = 30. Therefore, the distance from the foot of the ladder to the building is 30 feet.
The correct answer is option c. 30.