Angles of Elevation and Depression?

M

mdsirleaf

New member
A 10-foot ladder is placed against the side of a building, The bottom of the ladder is 8 feet from the base of the building. In order to increase the reach of the ladder against the building, it is moved 4 feet closer to the base of the building,. To the nearest foot, how much further up the building does the ladder now reach?
thanks very much
 
You can actually use Pythagorean theorem to solve this, not necessary to introduce any angles. Here's how:

Initially, the 10-foot ladder forms the hypotenuse of a right triangle that has a horizontal leg of 8 (the ground). Using Pythagorean, you find the ladder is 6 feet up the wall of the building.

If it is moved 4 feet *closer* to the building, it is now 8-4 = 4 feet from the base of the building. The hypotenuse (ladder) is still 10. Using Pythagorean theorem where x is the height the top of the ladder reaches on the building wall:

x² + 4² = 100²
x² = 84
x = 2?21 ? 9.17 ft.

So if the ladder was originally 6 feet high on the wall and increased to 9.17 feet high on the wall, it is 3.17 feet further up the wall. Good question!!
 
You can actually use Pythagorean theorem to solve this, not necessary to introduce any angles. Here's how:

Initially, the 10-foot ladder forms the hypotenuse of a right triangle that has a horizontal leg of 8 (the ground). Using Pythagorean, you find the ladder is 6 feet up the wall of the building.

If it is moved 4 feet *closer* to the building, it is now 8-4 = 4 feet from the base of the building. The hypotenuse (ladder) is still 10. Using Pythagorean theorem where x is the height the top of the ladder reaches on the building wall:

x² + 4² = 100²
x² = 84
x = 2?21 ? 9.17 ft.

So if the ladder was originally 6 feet high on the wall and increased to 9.17 feet high on the wall, it is 3.17 feet further up the wall. Good question!!
 
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