SOLUTION: please help me to solve the following word problem. A 20 foot ladder is leaned against a wall. If the base of the ladder is 8 feet from the wall, how high up the wall will the la

Algebra ->  Pythagorean-theorem -> SOLUTION: please help me to solve the following word problem. A 20 foot ladder is leaned against a wall. If the base of the ladder is 8 feet from the wall, how high up the wall will the la      Log On


   

Question 552515: please help me to solve the following word problem. A 20 foot ladder is leaned against a wall. If the base of the ladder is 8 feet from the wall, how high up the wall will the ladder reach?
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
please help me to solve the following word problem. A 20 foot ladder is leaned against a wall. If the base of the ladder is 8 feet from the wall, how high up the wall will the ladder reach?
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Use Pythagoras
h%5E2+=+20%5E2+-+8%5E2
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How is that a "word problem?"

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see the diagram:
$$$$$
AC is the length of the ladder
BC is the distance of the ladder from the wall.
AB is the height of the ladder on the wall.
angle (ACB) = angle that ladder makes with the ground.
cosine (ACB) = adjacent / hypotenuse = 8/20.
ACB = arc cosine (8/20) = 66.42182152 degrees.
sine (ACB) = sine (66.42182152) = .916515139
sine (ACB) = opposite / hypotenuse = AB / AC = AB / 20
solve for AB to get:
AB = 20 * sine (ACB) which makes:
AB = 20 * .916515139 which makes:
AB = 18.33030278