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A 25 foot ladder is set against the side of a house so that it reaches up 15 feet. If Camden grabs the ladder at its base and pulls it 3 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 12 ft.) Round to the nearest tenth of a foot.

Sagot :

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

View image MrRoyal

Answer:

9.8 FT

Step-by-step explanation:

its right