The distance between the point of the base of the building to the point where the ladder touches it for this case is 13.14 ft approx.
What is Pythagoras Theorem?
If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]
where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).
Consider the diagram attached below.
We've got:
- |AC| = length of the ladder = 15.5 ft
- |BC| = distance of base of ladder from the base of building = 8.2 ft
- |AB| = length we need
Usually buildings are vertical, so perpendicular to the ground.
Therefore, we can take ABC a right angled triangle, and therefore, use Pythagoras theorem here:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\15.5^2 = |AB|^2 + 8.2^2\\|AB|^2= 240 - 67.24\\\\|AB| = \sqrt{172.76} \approx 13.14 \: \rm ft[/tex]
(took only positive root as length cannot be negative).
Thus, the distance between the point of the base of the building to the point where the ladder touches it for this case is 13.14 ft approx.
Learn more about Pythagoras theorem here:
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