The double ladder

The double ladder has 3 meters long shoulders. What is the height of the upper of the ladder reach if the lower ends are 1.8 meters apart?

Result

x =  2.862 m

Solution:

a=3 m b=1.8/2=910=0.9 m  a2=b2+x2 x=a2b2=320.922.86182.862 ma=3 \ \text{m} \ \\ b=1.8/2=\dfrac{ 9 }{ 10 }=0.9 \ \text{m} \ \\ \ \\ a^2=b^2 + x^2 \ \\ x=\sqrt{ a^2-b^2 }=\sqrt{ 3^2-0.9^2 } \doteq 2.8618 \doteq 2.862 \ \text{m}



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