A painter leans a 20-ft ladder against a building. The base of the ladder is 12 ft from the building. To the nearest foot, how h
igh on the building does the ladder reach?
2 answers:
<h2>Answer:</h2>
The height of the building to which the ladder reaches is:
16 ft.
<h2>Step-by-step explanation:</h2>We can model this problem with the help of a right angled triangle ΔABC such that the hypotenuse of the triangle is 20-ft and one of it's leg is: 12 ft.
Now we are asked to find the other leg of the triangle.
We will use the Pythagorean Theorem in order to find the other leg.
Pythagorean Theorem says that: If c is the hypotenuse of the right triangle and a and b are it's two legs then,
Hence, here we have:
So,
Since, b can't be negative as it denotes a side of a triangle.
Hence, we get:
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Answer:
We want to find:
Here we can use Stirling's approximation, which says that for large values of n, we get:
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
Now we can just simplify this, so we get:
And we can rewrite it as:
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus: