Let the distance between the tree and the first point (point H) be x and let the height of the tree be h, then:
[tex]\tan40^o= \frac{h}{x} \\ \\ \Rightarrow h=x\tan40^o \ . \ . \ . \ (1) [/tex]
Also, the distance from the tree to the second point (point L) is x + 60, thus:
[tex]\tan30^o= \frac{h}{x+60} \\ \\ \Rightarrow h=(x+60)\tan30^o \ . \ . \ . \ (2) [/tex]
From (1) and (2), we have:
[tex]x\tan40^o=(x+60)\tan30^o \\ \\ \Rightarrow 0.8391x=0.5774x+34.64 \\ \\ \Rightarrow0.2617x=34.64 \\ \\ \Rightarrow x= \frac{34.64}{0.2617} =132.4 \ feet[/tex]
From (1):
h = x tan 40° = 132.4 (0.8391) = 111.1 feet.
Therefore, the height of the tree is 111.1 feet
