SOLUTION: A 25-foot ladder leaning against a building touches the wall 16 feet above the ground. How far from the building is the bottom of the ladder?

Question 88645: A 25-foot ladder leaning against a building touches the wall 16 feet above the ground. How far from the building is the bottom of the ladder?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
We basically have this triangle set up:

Since we can see that the triangle has legs of 16 and x with a hypotenuse of 25, we can use Pythagoreans theorem to find the unknown side.

Pythagoreans theorem:

where a and b are the legs of the triangle and c is the hypotenuse

Plug in a=16, b=x, and c=25. Now lets solve for x

Square each individual term

Subtract 256 from both sides

Combine like terms

Take the square root of both sides

Simplify the square root

Which approximates to...

So our answer is

So the bottom of the ladder is about 19.21 feet from the building
RELATED QUESTIONS
a 15 foot ladder leaning against a building touches the wall 12 feet above the ground.... (answered by tommyt3rd,Alan3354)

A 25-foot ladder leaning against a building touches the wall 18 feet above the ground.... (answered by checkley75)

A 16 foot ladder is leaning up against a building, 7 feet from the wall. How highs the... (answered by nerdybill)

a 20 foot ladder leaning against the building reches a point 16 feet above the ground.... (answered by rfer)

my question says: A 26 foot ladder is leaning against a building. The foot of the ladder... (answered by CharStar)

3. A 20 ft. ladder is placed against the wall of building the ladder touches the building (answered by mananth)

A 45-foot ladder leans against a building point 27 feet above the ground. How far is the... (answered by jorel1380)

A ladder is leaning against the side of a building. Each time I step from one rung to... (answered by TimothyLamb)

An 18-foot ladder is leaning against a wall where it makes an angle of 58° with the... (answered by josgarithmetic)