how many feet from the base of a house must a 39-foot ladder be placed so that the top of the ladder will reach a point on the house 36 feet from the ground
when you place the ladder on the house, it forms a right triangle, where the length of ladder is the hypotenuse.
recall Pythagorean theorem:
c^2 = a^2 + b^2
where c = hypotenuse, and a and b are the legs
substituting (letting a = 36),
39^2 = 36^2 + b^2
1521 = 1296 + b^2
1521 - 1296 = b^2
225 = b^2
b = sqrt(225) = 15 ft
hope this helps~ :)
To determine the distance from the base of the house where the ladder should be placed, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, the distance from the base of the house to the point on the house where the ladder reaches is one side, and the height from the ground to that point is the other side.
Let's assume x represents the distance from the base of the house where the ladder should be placed.
According to the Pythagorean theorem:
x^2 + 36^2 = 39^2
To solve for x, we can rewrite the equation as:
x^2 + 1296 = 1521
Subtracting 1296 from both sides:
x^2 = 225
Taking the square root of both sides:
x = 15
Therefore, the ladder should be placed 15 feet from the base of the house.
To answer this question, we can use the Pythagorean theorem, which states that in a right-angled 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, the height of the house is one side, and the distance from the house is the other side.
Let's denote the distance from the base of the ladder to the house as "x." Using the Pythagorean theorem, we can set up the equation:
x^2 + 36^2 = 39^2
Simplifying the equation, we have:
x^2 + 1296 = 1521
x^2 = 1521 - 1296
x^2 = 225
To find the value of x, we take the square root of both sides of the equation:
x = √225
x = 15
Therefore, the ladder must be placed 15 feet from the base of the house in order for the top of the ladder to reach a point on the house 36 feet from the ground.