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
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-> 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
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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 3 solutions by Alan3354, Theo, ikleyn:Answer by Alan3354(69443) (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
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How is that a "word problem?"
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
You can put this solution on YOUR website! .
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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This can be done much more quickly and more effectively than another tutor would do.
You have a right-angled triangle.
Its hypotenuse is the ladder length of 20 ft.
One leg of this right-angled triangle is 8 ft long.
It is the distance on the ground from the base of the ladder to the wall
You want to find how high up the wall will the ladder reach.
This length is another leg of this right-angled triangle.
We find this height by applying the Pythagorean formula
height = = = = 18.3303 ft.
Round and get the ANSWER: the ladder reaches the wall at the height of 18.33 ft.
Solved.
It is a standard mantra to pronounce when solving this problem.
