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To measure the height of a tree, a surveyor walked a short distance from the tree and found the angle of elevation was 43.9°, then walked 20 feet farther and measured the angle of elevation to be 37.6°. Find the height of the tree.

Respuesta :

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

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