A 16-ft ladder is placed 4-ft from the base of the building. How high on the building will the ladder reach?
4^2 + h^2 = 16^2
h^2 = 256 - 16 = 240 = 16*15
h = 4 sqrt 15
h = 15.5
To find the height on the building that the ladder will reach, we can use the Pythagorean theorem. The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
Where c is the hypotenuse (the length of the ladder), and a and b are the other two sides of the right triangle formed by the ladder, the base of the building, and the height on the building.
In this case, the length of the ladder (c) is 16 ft, and the distance from the base of the building to the ladder (a) is 4 ft. We need to find the height on the building (b).
Using the Pythagorean theorem, we can substitute the given values into the formula:
16^2 = 4^2 + b^2
Simplifying:
256 = 16 + b^2
Now, let's isolate b^2:
b^2 = 256 - 16
b^2 = 240
Take the square root of both sides to solve for b:
b = √240
b ≈ 15.49
So, the ladder will reach a height of approximately 15.49 ft on the building.
To determine how high the ladder will reach on the building, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). In this case, the ladder is the hypotenuse, and the distance from the base of the building to the ladder is one side, while the height on the building is the other side. Let's call the height on the building "h."
So, we have:
c² = a² + b²
In this scenario, the ladder (c) is 16 feet and the distance from the base of the building to the ladder (a) is 4 feet. We want to find the height on the building (h), which is equivalent to the other side (b).
Plugging in the known values into the equation, we have:
16² = 4² + h²
256 = 16 + h²
Next, we subtract 16 from both sides of the equation:
256 - 16 = h²
240 = h²
To solve for "h," we take the square root of both sides of the equation:
√240 = √h²
h ≈ 15.49
Therefore, the ladder will reach approximately 15.49 feet high on the building.