Answer:
Step-by-step explanation:
Check attachment for diagram
From the attachment we can apply trigonometry to find the distance of the person from the redwood. And we assume that the person height is negligible
Then, applying Tangent
Tanθ = opposite / adjacent
Tan60 = 370 / x
Cross multiply
Tan60 × x = 370
Divide both sides by Tan60
x = 370 / Tan60
x = 370 / √3
Taking conjugate
x = 370√3 / 3 ft
x = 640.86 ft.
So, he is 640.86 ft from the base of the tree.
As an observers distance from the base of the tree increases, the angle of
elevation to the top of the tree decreases.
The distance from the base of the tree the person is standing is approximately 213.62 feet.
Reasons:
The given parameter are;
The height of the giant redwood tree, h = 370-foot
Angle of elevation to the top of the tree, θ = 60°
Required:
The distance from the base of the tree.
Solution:
Let x represent the distance from the base of the tree, we have;
[tex]tan(\theta) = \mathbf{ \dfrac{h}{x}}[/tex]
Which gives;
[tex]x= \mathbf{\dfrac{h}{tan(\theta) }}[/tex]
Plugging in the values gives;
[tex]x= \dfrac{370 \ ft.}{tan(60 ^{\circ}) } \approx \mathbf{213.62 \, ft.}[/tex]
The distance from the base of the tree the person is standing, x ≈ 213.62 ft.
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