Question

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Posting the same question again ....


a ladder kept inclined at angle of 40°at a distance of 8 feet from the building touches the building at some height.If the same let it is kept at a distance of 6 feet with an inclination of 50° then find the height at which the ladder touches the building..

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Answer 1

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Answer 2

Answer:

8 ft.

Step-by-step explanation:

Let the  length of  ladder  be  x and  height  that  ladder  touches the  building in second  case  be  h.

In First  Case:

In ΔABC,

$\cos40\textdegree=\frac{AB}{AC}\\\;\\\cos40\textdegree=\frac{8}{x}\\\;\\\sin(90-40)\textdegree=\frac{8}{x}\\\;\\\sin50\textdegree=\frac{8}{x}\;\;\;...........i)$

In Second  Case:

In ΔDEF

$\sin50\textdegree=\frac{FE}{DE}\\\;\\\sin50\textdegree=\frac{h}{x}\\\;\\\frac{8}{x}=\frac{h}{x}\;\;\;\;\;\;\text{(Using eq. i)}\\\;\\h=8\;\;ft.$