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Answer:
The ladder will reach a height of 9.8 foot
Step-by-step explanation:
Given
Initial Position
[tex]L = 25ft[/tex] --- Length of the ladder
[tex]h = 15ft[/tex] --- height against the wall
New position
[tex]L = 25ft[/tex] --- Length of the ladder
[tex]B = 3ft[/tex] --- 3 feet farther from the wall
Required
Determine the new height the ladder will reach
The question is illustrated using the attached image.
Where
[tex]\triangle ABC[/tex] represents the initial position of the ladder
[tex]\triangle DBE[/tex] represents the new position of the ladder
The new height is represented with BD
Using Pythagoras theorem on [tex]\triangle DBE[/tex]
[tex]DE^2 = BE^2 + BD^2[/tex]
[tex]BE = BC + CE = 20 + 3 = 23[/tex]
[tex]BD = x[/tex]
[tex]DE =25[/tex] --- length of the ladder
So, the expression becomes
[tex]25^2 = 23^2 + x^2[/tex]
[tex]625 = 529 + x^2[/tex]
Collect like terms
[tex]x^2 = -529 + 625[/tex]
[tex]x^2 = 96[/tex]
Take positive square roots of both sides
[tex]x = \sqrt{96[/tex]
[tex]x = 9.8ft[/tex] --- approximated
