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Hey there!
First imagine this ladder as a right triangle, the length, 12 would be the slant height, the distance from the house, 5 would be the base length, and the height of how far up the ladder reaches would be the height of the triangle.
To represent this missing height, you can define it as the x variable.
Now, to solve for this x variable, you must use the Pythagorean theorem:
a^2+b^2=c^2
a and b are the two legs, and c is the slant length.
Now, plug in your known values:
(5)^2+(x)^2=(12)^2
Now, simplify:
25+x^2=144
Now, solve for x:
25+x^2=144
x^2=119
x=[tex] \sqrt{119} [/tex]
x is about 10.9.
Therefore, your final answer would be that the ladder reaches approximately 10.9 feet up the house.
First imagine this ladder as a right triangle, the length, 12 would be the slant height, the distance from the house, 5 would be the base length, and the height of how far up the ladder reaches would be the height of the triangle.
To represent this missing height, you can define it as the x variable.
Now, to solve for this x variable, you must use the Pythagorean theorem:
a^2+b^2=c^2
a and b are the two legs, and c is the slant length.
Now, plug in your known values:
(5)^2+(x)^2=(12)^2
Now, simplify:
25+x^2=144
Now, solve for x:
25+x^2=144
x^2=119
x=[tex] \sqrt{119} [/tex]
x is about 10.9.
Therefore, your final answer would be that the ladder reaches approximately 10.9 feet up the house.
The height of the house is [tex]10.9[/tex] feet, i.e. [tex]10.9[/tex] feet up ladder reach the house.
What is Pythagoras theorem ?
Pythagoras theorem states that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
i.e.
Pythagoras theorem: [tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]
i.e. [tex]H^2=P^2+B^2[/tex]
We have,
Length of ladder [tex](H)=12[/tex] feet
Distance between house and base of ladder [tex](B)=5[/tex] feet
Let, Height at which ladder reach the house [tex](P)=h[/tex] feet
So,
Using the Pythagoras theorem;
[tex]H^2=P^2+B^2[/tex]
So,
[tex]12^2=h^2+5^2[/tex]
[tex]144=h^2+25[/tex]
⇒ [tex]h^2 =119[/tex]
[tex]h=10.9[/tex] feet
So, the height of house is [tex]10.9[/tex] feet.
Hence, we can say that the height of the house is [tex]10.9[/tex] feet, i.e. [tex]10.9[/tex] feet up ladder reach the house.
To know more about Pythagoras theorem click here
https://brainly.com/question/343682
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