Question

A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot.

a.4.1 feet
b.17.0 feet
c.20.6 feet
d.21.4 feet

Answer 1

sorry im late but the answer is C. 20.6

Explanation:

Answer 2

c. 20.6 feet

Explanation:

Ok, take at look at the picture I attached you. As you can see, the length of the ladder, the distance from the floor to the top of the ladder and the distance from the building to the base of the ladder, together, form a right-angled triangle. So, in order to find how high up on the building does the ladder reach, we need to find the height h using Pythagorean Theorem:

`a^2+b^2=c^2`

Where:

`c=Length\hspace{3}of\hspace{3}the\hspace{3}hypotenuse`

`a\hspace{3}and\hspace{3}b\hspace{3}are\hspace{3}the\hspace{3}lengths\hspace{3}of\hspace{3}the\hspace{3}remaning\hspace{3}two\hspace{3}sides`

So, let:

`b=4ft`

`a=h`

and we know:

`c=21ft`

Replacing the data in the equation:

`21^2=h^2+4^2`

Solving for h:

`h^2=21^2-4^2\\√(h^2) =√(441-16) \\h=√(425) \\h=20.61552813ft\approx20.6ft`