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A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet. What is the height of the ladder?

A ladder is placed 8 feet away from a wall The distance from the ground straight to the top of the wall is 16 feet What is the height of the ladder class=

Respuesta :

wegnerkolmp2741o

Answer:

17.89 ft

Step-by-step explanation:

This is a right triangle so we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

8^2 +16^2 = c^2

64+ 256 = c^2

320 =c^2

Taking the square root of each side

sqrt(320) = sqrt(c^2)

sqrt(64*5) = c

sqrt(64) sqrt(5) =c

8 sqrt(5) = c

17.88854382=c

17.89 ft

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QueenOfAttitude

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

Given:-

  • A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet.

Find:-

  • What is the height of the ladder?

solution:-

A ladder is placed 8 feet away from a wall. The distance from the ground straight to the top of the wall is 16 feet.

so it is a right angle triangle

we know that,

in a right angle triangle, According to the Pythagorean theorom,

[tex]\boxed{\sf{l^2+b^2=h^2 }}[/tex]

where

  • l= legs
  • b=base
  • h=hypotenuse

According to the question,

  • [tex]\sf{8^2+16^2=h^2 }[/tex]

  • [tex]\sf{64+256=h^2 }[/tex]

  • [tex]\sf{ h^2=320 }[/tex]

  • [tex]\sf{h=\sqrt{320} }[/tex]

  • [tex]\sf{h=8\sqrt{5} }[/tex]

Therefore:-

The height of the ladder is [tex]\sf{8\sqrt{5} }[/tex]

Ver imagen QueenOfAttitude

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