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A ladder 24 ft long is leaning against a sloping embankment. The foot of the ladder is 11 ft from the base of the embankment, and the distance from the top of the ladder down the embankment to the ground is 16 ft. What is the angle at which the embankment is inclined to the horizontal?

 May 24, 2020
 #1
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A ladder 24 ft long is leaning against a sloping embankment. The foot of the ladder is 11 ft from the base of the embankment, and the distance from the top of the ladder down the embankment to the ground is 16 ft. What is the angle at which the embankment is inclined to the horizontal?

 

Hello Guest!

 

x is the distance between the vertical under the top point of the ladder and the bottom point of the slope.

 

\(h^2=16^2-x^2\\ h^2=24^2-(11+x)^2\\ 16^2-x^2=24^2-121-22x-x^2\\ 22x=24^2-121-16^2\\ 22x=199\)

\(x=9.0\overline{45}\)

\(cos(\alpha)=\dfrac{x}{16}\\ cos(\alpha)=\dfrac{9,0\overline{45}}{16}\\ \alpha=arc cos(\dfrac{9,0\overline{45}}{16})\)

\(\alpha=55.574\ ^0\)          \(180\ ^0-55.574\ ^0=124.426\ ^0=124\ ^025'\ 33''\)

 

The slope slopes away from the plain at an angle of \(124\ ^025'\ 33''\).

laugh  !

 May 24, 2020
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The rain in Spain falls mainly in the plane. 

Guest May 24, 2020

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