Question

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.

Answer 1

Answer:

The ladder will reach a height of 9.8 foot

Step-by-step explanation:

Given

Initial Position

$L = 25ft$ --- Length of the ladder

$h = 15ft$ --- height against the wall

New position

$L = 25ft$ --- Length of the ladder

$B = 3ft$ --- 3 feet farther from the wall

Required

Determine the new height the ladder will reach

The question is illustrated using the attached image.

Where

$\triangle ABC$ represents the initial position of the ladder

$\triangle DBE$ represents the new position of the ladder

The new height is represented with BD

Using Pythagoras theorem on $\triangle DBE$

$DE^2 = BE^2 + BD^2$

$BE = BC + CE = 20 + 3 = 23$

$BD = x$

$DE =25$ --- length of the ladder

So, the expression becomes

$25^2 = 23^2 + x^2$

$625 = 529 + x^2$

Collect like terms

$x^2 = -529 + 625$

$x^2 = 96$

Take positive square roots of both sides

$x = \sqrt{96$

$x = 9.8ft$ --- approximated

Answer 2

Answer:

9.8 FT

Step-by-step explanation:

its right