Answer:
The height of the tree is H = 77.06 m
Step-by-step explanation:
From Δ ABC
AB = height of the tree
[tex]\tan 43.9 = \frac{AB}{BC}[/tex]
[tex]\tan 43.9 = \frac{h}{x}[/tex]
h = 0.9623 x ------- (1)
From Δ ABD
[tex]\tan 37.6 = \frac{h}{20+ x}[/tex]
h = 0.77 (x + 20) ----- (2)
Equating Equation 1 & 2 we get
0.9623 x = 0.77 (x + 20)
0.9623 x = 0.77 x + 15.4
x (0.1923) = 15.4
x = 80.08 m
Thus the height of the tree is given by
H = 0.9623 x
H = 0.9623 × 80.08
H = 77.06 m
Therefore the height of the tree is H = 77.06 m
