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A ladder is leaning against the side of a building and positioned such that the base of the ladder is 17 ft from the base of the building. If the
ladder reaches 23 ft above the ground, how long is the ladder. Round your answer to the nearest tenth

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Answer:

The ladder is 28.6 feet long.

Step-by-step explanation:

Given that:

Length of base = 17 feet

Length above the ground = 23 feet

These forms two legs of right angled triangle.

The length of ladder will be the hypotenuse.

Using Pythagorean theorem;

[tex]a^2+b^2=c^2\\(17)^2 + (23)^2 = c^2 \\289 + 529 = c^2 \\c^2 = 818[/tex]

Taking square root on both sides

[tex]\sqrt{c^2}=\sqrt{818}\\c=28.6[/tex]

Hence,

The ladder is 28.6 feet long.

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