Question

If the ladder is 16 feet long and the window ledge is 12 feet off the ground, how far from
the house is the base of the ladder?

Answer 1

Answer:

10.58 feet

Step-by-step explanation:

Hello!

If you think about how it would look in life you will notice that it looks like a right triangle which means we can use the Pythagorean theorem to find the far the ladder needs to be from the house.

The Pythagorean theorem is $a^{2}+ b^{2}= c^{2}$

a is a leg

b is the other leg

c is the hypotenuse

Since the ladder has to go from the ground to the window ledge it is the hypotenuse and the window ledge is a leg

Put in what we know

$a^{2} +12^{2} =16^{2}$

Now we solve for a

Simplify

a^2 + 144 = 256

Subtract 144 from both sides

a^2 = 112

Take the square root of both sides

a = 10.583

The answer is 10.58 feet

Hope this helps!

Answer 2

Answer:

11 ft

Step-by-step explanation:

Try to imagine it or draw it out to help you. The ladder is 16 feet long and the window ledge is 12 feet high, so this is a right triangle.

The ladder is the hypotenuse, so use the given values in the pythagorean theorem.

a^2 + b^2 = c^2

12 + b^2 = 16

b = 11

12^2 + 11^2 = 16^2

1 44 + 121 = 265

√265 = 16