Answer:
33.6 feet
Step-by-step explanation:
Given : An ant looks up to the top of a tree with an angle of elevation of 38.
To Find: If the ant is 43 feet from the base of the tree, what is the height of the tree, to the nearest tenth?
Solution:
Refer the attached figure
An ant looks up to the top of a tree with an angle of elevation of 38.i.e.∠ACB= 38°
The ant is 43 feet from the base of the tree i.e.BC = 43 feet.
Now we are supposed to find the height of the tree i.e. AB
Now we will use trigonometric ratio
[tex]Tan \theta = \frac{Perpendicular}{Base}[/tex]
[tex]Tan 38^{\circ} = \frac{AB}{BC}[/tex]
[tex]Tan 38^{\circ} = \frac{AB}{43}[/tex]
[tex]0.78128= \frac{AB}{43}[/tex]
[tex]0.78128 \times 43= AB[/tex]
[tex]33.6= AB[/tex]
Hence the height of the tree is 33.6 feet.
