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a painter has a 24-foot ladder that he is using to paint a house. for safety reasons, the ladder must be placed at least 8 feet from the base of the side of the house. to the nearest tenth of a foot , how high can the ladder safety reach?

Respuesta :

dexteright02
The Pythagorean Theorem states that: "the sum of the squares of the legs is equal to the square of the hypotenuse." 
a² + b² = c² or  c² = a² + b²

Note¹: Hypotenuse is the side opposite the right angle.
Note²: The legs are the sides that are not opposite the right angle.
Note³: The sloping ladder leaning against the side of the house forms a right angle.

Solving

Data:
c = 24 ft
a = 8 ft
b = ?

Solving:
[tex]c^2 = a^2 + b^2[/tex]
[tex]24^2 = 8^2 + b[/tex]
[tex]576 = 64 + b^2[/tex]
[tex]b^2 = 576 - 64[/tex]
[tex]b^2 = 512[/tex]
[tex]b = \sqrt{512} [/tex]
[tex]b = 22.627417 \to \boxed{\boxed{b \approx 22.6}}\end{array}}\qquad\quad\checkmark[/tex]

Answer:
The ladder for safety will be at a height of approximately 22.6 feet
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