Question

What is the maximum height that a 24 foot ladder can safely reach if the base of the ladder should always be about 1 foot away from the vertical support for every 4 feet of height?

Answer 1

23.24 feet

Explanation:

According to the question, we were asked to find the maximum height that a 24 foot ladder can safely reach if the base of the ladder should always be about 1 foot away from the vertical support for every 4 feet of height.

-------The ladder is 24 feet high

------- There should be a spacing of 1 foot from the vertical support for every 4 feet height of the ladder

Which means that if the ladder is a feet tall,a spacing of 1 foot from the vertical support should be maintained and if it's an 8 feet tall ladder,then a spacing of 2 feet and so on.

Since the ladder is 24 feet tall and for every 4 feet tall ladder, a spacing of 1 foot should be reached.

Therefore, for a ladder of 24 feet,the spacing will be

24/4 = 6 feet

If this ladder is leaned against a wall and the spacing of 6 feet against its vertical support is maintained we are going to have a shape of a right angled triangle formed by the ladder against the support.

And we are now to find out how long the ladder will make it against its vertical support.

---- We are going to use the Pythagorean theorem to calculate this problem.

The requirements are the hypotenuse,c, the base,b,of the triangle and the other side also known as the opposite,a.

C² = a² + b²

a² = c² - b²

a = √c² - b²

a = √ 24² - 6²

a = √540

a= 23.24 feet.

Therefore, the height that the ladder makes against its vertical support is 23.24 feet

Answer 2

Answer: The maximum height it can safely reach is 23 feet (approximately)

Step-by-step explanation: First of all the ladder is 24 feet long. Then it needs to rest on a vertical support and it is recommended that for every 4 feet the ladder goes up, there should be a 1 foot safety distance between the base of the ladder and the vertical support. In other words, if the whole length of the ladder were to be placed on the vertical support, the 24-foot height must have a safety distance of,

Base = height/4

Base = 24/4

Base = 6

What this implies is that, as long as the whole length of the ladder (24 ft) is placed on the support, the safe distance from the base of the support would be 6 feet. At this rate, the maximum height that the ladder can reach is simply the vertical support itself. This results in a right angled triangle with hypotenuse 24 ft, and one side measuring 6ft. The unknown side can be derived by use of the Pythagoras theorem which states that,

AC^2 = AB^2 + BC^2

Where AC is the hypotenuse and AB and BC are the other two sides.

We can now substitute for the values as follows,

24^2 = 6^2 + BC^2

576 = 36 + BC^2

Subtract 36 from both sides of the equation

540 = BC^2

Add the square root sign to both sides of the equation

BC = 23.2379

By approximation, BC equals 23 feet.

That means the maximum height the ladder can SAFELY reach is 23 feet.