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Question 80533: A wooden board is placed so that it leans against a loading dock to provide a ramp.
The board is supported by a metal beam perpendicular to the ramp and placed on a 1 ft. tall support.
The bottom of the support is 7 feet from the point where the ramp meets the ground. The slope of the ramp is 2/5.
Find the length of the beam to the nearest hundredth of a foot. Note that the 1 ft. support is vertical, but the metal beam is not.
Could you also show how you got this answer?THx
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A wooden board is placed so that it leans against a loading dock to provide a ramp.
The board is supported by a metal beam perpendicular to the ramp and placed on a 1 ft. tall support.
The bottom of the support is 7 feet from the point where the ramp meets the ground. The slope of the ramp is 2/5.
Find the length of the beam to the nearest hundredth of a foot. Note that the 1 ft. support is vertical, but the metal beam is not.
Could you also show how you got this answer?THx
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Draw a coordinate system
Put the 1 ft. post on the y-axis with its base at the origin.
The ramp is a line segment from (0,7) toward the y-axis with
a slope of -2/5
The top of the post is at (0,1).
Draw a line segment from (0,1) perpendicular to the ramp.
You need to find that point of intersection of the ramp
and the post.
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Ramp equation:
slope = -2/5 and the line passes thru (7,0)
EQUATIon of the ramp: y=(-2/5)x+14/5
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Equation of line perpendicular to the ramp:
slope = 5/2 and the line passes thru (0,1)
EQUATION of that line: y=(5/2)x+1
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Find the intersection of these two equations:
(-2/5)x+14/5 = (5/2)x+1
(-2/5-5/2)x=1-14/5
-29/10 x = -18/10
x=18/29
Now, solve for y:
y=(5/2)(18/29)+1
y = 45/29+29/29= 74/29
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Find the distance from (0,1) to (18/29,74/29)
d=sqrt[(18/29-0)^2 + (74/29-1)^2]
d=sqrt2.7931...
d=1.671258... ft.
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Cheers,
Stan H.
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