SOLUTION: For safety reasons, the base of a 26 foot ladder should be at least 8 feet from the wall.How high can a 26 foot ladder safely reach?

Question 117600: For safety reasons, the base of a 26 foot ladder should be at least 8 feet from the wall.How high can a 26 foot ladder safely reach?
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 x and 8 with a hypotenuse of 26, 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=x, b=8, and c=26. Now lets solve for x

Square each individual term

Subtract 64 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 ladder can reach about 24.74 feet
RELATED QUESTIONS
a 26 foot ladder rest against a wall with the bottom of the ladder 7 feet from the base... (answered by doctor_who)

how far from the base of the building must a 26 foot ladder be placed so that it reaches... (answered by user_dude2008)

A painter leans a 26-foot extension ladder against a building, with the base 10 feet... (answered by mananth)

How high up a vertical wall will a 26-foot-long extension ladder reach if its base is... (answered by josmiceli,MathLover1)

please help me to solve the following word problem. A 20 foot ladder is leaned against a (answered by Alan3354,Theo)

For safety, a ladder should be at least 1ft from the wall for every 3ft of ladder. How... (answered by ankor@dixie-net.com)

A 15 foot ladder leans up against a building, The foot of the ladder is 5 feet from the... (answered by JulietG)

A 26-foot ladder is placed against a vertical wall of a building, with the... (answered by advanced_Learner,ikleyn)

A 25 foot ladder is placed 7 feet from base of a wall. How high up the wall can the... (answered by rfer)