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Q: How far up a wall will a 10-meter ladder reach if the foot of the ladder is 5 meters away from the base of the wall?

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Use the cosine ratio: 5.437846722 meters

Using Pythagoras' theorem the length of the ladder is 20.248 feet

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This question is where you use the Pythagorean Theorem. Go to http://en.wikipdedia.org/ and search for Pythagorean Theoremif you don't already remember what it is, and good luck.

9.2

Use the cosine ratio: 5.437846722 meters

The ladder is 7 foot up the wall if the ladder if the ladder is 3 ft away from wall.

10,000 m

Using Pythagoras' theorem the length of the ladder is 20.248 feet

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No. if the floor is smooth you must have friction between the ladder and the floor, or the ladder would just slide away. Technically you could do without friction between wall and ladder, but even that can be helpful in preventing the ladder from going sideways.

The slope is 4 (no units), and the ladder is 16.492 feet long. (rounded)

Perfume evaporates, the perfume molecules diffuse through the air and reach your nose, enabling you to smell them.

"A few meters away from our home" is not a correct grammar but the correct one is "Few meters away from our home."