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Answer:
Step-by-step explanation:
The formula that relates the length of a ladder, L, that leans against a wall with distance d from the base of the wall and the height h that the ladder reaches up the wall is L = StartRoot d squared + h squared EndRoot. What height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base of a wall?
L = √d² + h²
Height is equal to [tex]14.59[/tex] feet
Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle).
[tex]l=\sqrt{h^2+d^2}[/tex]
[tex]l=15[/tex] feet
[tex]d=3.5[/tex] feet
[tex]15=\sqrt{3.5^2+h^2}[/tex]
[tex]15=\sqrt{12.25+h^2}[/tex]
[tex]225=12.25+h^2[/tex]
[tex]212.75=h^2[/tex]
[tex]\sqrt{212.75}=h[/tex]
[tex]h\approx 14.59[/tex] feet
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