Answer:
The correct option is C. 50 feet.
Therefore the girl is 50 feet away from the tree.
Step-by-step explanation:
Consider a Right angle Triangle
Elevation to the tree is ' θ '
Adjacent Side to θ = distance from the tree to girl = distance
Opposite Side to θ = height of the tree = height
[tex]\tan \theta =\dfrac{20}{50}[/tex]
To Find:
distance from the tree to girl = distance
Solution:
In Right angle Triangle Tangent Identity
[tex]\tan \theta = \dfrac{\textrm{side opposite to angle theta}}{\textrm{side adjacent to angle theta}}[/tex]
Substituting we get
[tex]\tan \theta = \dfrac{\textrm{height of the tree}}{\textrm{distance from the tree to girl}}[/tex]
[tex]\tan \theta = \dfrac{height}{distance}[/tex]
[tex]\tan \theta =\dfrac{20}{50}[/tex] ........Given
Comparing the given equation with the above we get
[tex]distance =50\ feet[/tex]
Therefore the girl is 50 feet away from the tree.
