Question

10. Assuming that a 370-foot tall giant redwood grows vertically, if I walk a certain distance from the tree and measure the angle of elevation to the top of the tree to be 60°, how far from the base of the tree am I?

Answer 1

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.

Answer 2

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;

$tan(\theta) = \mathbf{ \dfrac{h}{x}}$

Which gives;

$x= \mathbf{\dfrac{h}{tan(\theta) }}$

Plugging in the values gives;

$x= \dfrac{370 \ ft.}{tan(60 ^{\circ}) } \approx \mathbf{213.62 \, ft.}$

The distance from the base of the tree the person is standing, x ≈ 213.62 ft.

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