Pat needs to determine the height of a tree before cutting i

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. The angle of elevation of the tree from one position on a flat path from the tree is H = 50degree: and from a second position L = 40 feet farther along this path it is B = 20degree. What is the height of the tree? The height of the tree is approximately

Solution

from the diagram

tanH= h/wx

=>tan50^o= h/wx

=>wx =h/tan50^o------------->(1)

tanB=h/(wx +L)

tan20^o=h/(wx +40)

wx+40=h/(tan20^o)----------->(2)

put (1) in(2)

(h/tan50^o)+40=(h/tan20^o)

(h/tan20^o)-(h/tan50^o) =40

h(tan50^o-tan20^o)/(tan20^otan50^o) =40

h=40(tan20^otan50^o)/(tan50^o-tan20^o)

h=20.96

height of tree =21.0 ft