How high up the wall does the ladder​ reach?

Lorrie places a 25​-foot ladder against the side of a building with the bottom of the ladder 7 feet from the base of the building. How high up the wall does the ladder​ reach?

The ladder reaches ______feet up the wall.

​(Round to the nearest whole number as​ needed.) 

Update:

 The surface area is______

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7 Answers

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  • 2 months ago

    (1) Let h feet be the height on the wall at which

    the ladder reaches.

    h=sqr(25^2-7^2)=24 ft.

    (2) The volume=pi(5^2)(7)/3=183.26 cm^3.

    The slant height of the cone=sqr(5^2+7^2)=

    8.6023 cm.

    The circumference of the base circle=

    2pi(5) cm.

    The surface area of the developed cone=

    (8.6023)(2pi(5))/2=43.0115pi cm^2

    The total surface area including the base=

    pi(5^2)+43.0115pi=68.0115pi=213.66 cm^2.

    Note that if the base area is not counted, then

    neglect pi(5^2).

  • David
    Lv 7
    2 months ago

    Using Pythagoras the ladder reaches exactly 24 feet up the wall

  • 2 months ago

    ((25+7)*(25-7))^(1/2)=24

    can you guess the steps involved?

  • 2 months ago

     Lorrie places a 25​-foot ladder against 

     the side of a building with the bottom of the ladder 

     7 feet from the base of the building. 

     How high up the wall does the ladder​ reach? 

     s² + b² = h²

     7² + b² = 25²

     49 + b² = 625

     b² = 576

     b = 24 ft

     The ladder reaches 24 feet up the wall.  ​

     Deterrmine the volume and the surface area of the three-dimensional figure. 

     a) 

     The volume is 183.26 cm^3 

     b) 

     The surface area is 213.66 cm^2

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  • alex
    Lv 7
    2 months ago

    Hint:

    1/

    Pythagorean Theorem

    2/

    Formula of the surface area

  • 2 months ago

    h = hypotenuse = length of ladder = 25 ft

    x = horizontal distance of the ladder's base from the building = 7 ft

    θ = angle that the ladder makes with the ground = to be determined

    y = vertical height of the ladder's opposite end = to be determined

    cos θ = x / h

    cos θ = 7 ft / 25 ft

    cos θ = 0.28

    θ = arccos( 0.28 )

    θ = 73.73979529 °

    sin θ = y / h

    h(sin θ) = y

    y = h(sin θ)

    y = (25 ft)(sin 73.7398°)

    y = 24 ft

  • 2 months ago

    If you sketch a diagram of the ladder against a wall, you end up with a right triangle with a base of 7 ft and a hypotenuse of 25 ft.  You can use the Pythagorean Theorem to find the unknown height:

    a² + b² = c²

    7² + b² = 25²

    49 + b² = 625

    b² = 576

    b = 24 ft

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