A7 feet ladder is leaning against the building. the foot of the ladder is 2 feet from the base of the building. how far up the wall is the top of the ladder

This problem is resolved with the Pythagorean Theoreme.

It states that the length of the side that is the hypotenuse (the side opposite the right angle) is equal to the square root of the sum of the length of the other two sides squared.

So we know that the ground and the building form the right angle, so the hypotenuse is the length of the ladder (L) and the building (B) and the ground (G) are the other sides of the triangle (legs). So by the pythagorean theoreme:

L = √ (G^2+B^2)

As we already know the length of the hypotenuse, we have to isolate the variable that we don’t know (B).

B = √(H^2-G^2)

Replacing:

B = √(7^2-2^2)
B= √(49-4)
B = √45
B = 6,7 feet

I hope you find my answer helpful.