Answer :
The height at which the ladder touch the wall when the ladder is 30 feet long, and the ladder is 10 feet from the base of the wall is 20√2 feet.
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 below.
We've got:
- Length of the ladder = |AC| = 30 ft
- Distance between ladder's bottom and base of wall = |BC| = 10 ft
- Height of wall from base to the point where ladder touches = |AB| is to be known.
The wall is usually perpendicular to ground, therefore making 90° angle with it. Thus, ABC is a right angled triangle.
Using Pythagoras theorem in it, we get:
[tex]|AC|^2 = |AB|^2 + |BC|^2\\\\30^2 = |AB|^2 + 10^2\\|AB|^2 = 900 - 100\\\\|AB|^2 = 800\\\\\text{Taking sq. root of both the sides}\\\\|AB| = \sqrt{800} = \sqrt{ (\pm 20\sqrt{2})^2}\\\\|AB| = \pm 20\sqrt{2} \: \rm ft[/tex]
But as length cannot be a negative quantity, so we get:
[tex]|AB| = 20\sqrt{2} \: \rm ft[/tex]
Thus, the height at which the ladder touch the wall when the ladder is 30 feet long, and the ladder is 10 feet from the base of the wall is 20√2 feet.
Learn more about Pythagoras theorem here:
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