lynn asked in Science & MathematicsMathematics · 2 months ago

# 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______

Relevance
• 2 months ago

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

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

• 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