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a ladder is 13 feet long and leans up against he side of a house. the house and the ground form a right angle. The bottom of the ladder is 5 feet from the house.



what is the distance between the ground and the top of the ladder, in feet?​

a ladder is 13 feet long and leans up against he side of a house the house and the ground form a right angle The bottom of the ladder is 5 feet from the housewh class=

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theleangreenbean

The Pythagorean Theorem

This theorem states that [tex]a^2+b^2=c^2[/tex], where c is the hypotenuse of a triangle and a and b are the legs (the other two sides).

Solution

As we can see from the image, we are given the lengths of the hypotenuse and one of the legs. Now, we must find x, the length of the other leg.

[tex]a^2+b^2=c^2[/tex]

Plug in the given lengths:

[tex]5^2+b^2=13^2[/tex]

Solve for b:

[tex]b=-12,12[/tex]

Since length cannot be negative, we know that b must be equal to 12.

Answer

x = 12 ft

The Pythagorean Theorem

This theorem states that , where c is the hypotenuse of a triangle and a and b are the legs (the other two sides).

Solution

As we can see from the image, we are given the lengths of the hypotenuse and one of the legs. Now, we must find x, the length of the other leg.

Plug in the given lengths:

Solve for b:

Since length cannot be negative, we know that b must be equal to 12.

Answer

x = 12 ft

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