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An arborist wants to prune an oak tree that has grown too tall. The arborist takes a 15-foot ladder and places it on a horizontal surface on the ground so it leans against the tallest part of the tree trunk. If the bottom part of the ladder makes an angle of 70 degrees with respect to the ground, what is the distance between the ladder and the tree trunk?

Respuesta :

calculista
see the attached picture to better understand the problem

we know that
in the right triangle ABC
cos 70=adjacent side angle 70/hypotenuse
adjacent side angle 70=BC----> distance between the ladder and the tree trunk
hypotenuse=AC------> 15 ft

cos 70=BC/AC-------> solve for BC
BC=AC*cos 70------> BC=15*cos 70-----> BC=5.13 ft

the answer is
the distance between the ladder and the tree  is 5.13 ft
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