Question

Can you help me for this? A tree needs to be staked down before a storm. If the ropes can be tied on the tree trunk 17 feet above the ground and the staked rope should make a 60° angle with the ground, how far from the base of the tree should each rope be staked? Round to the nearest foot?

Answer 1

Seeing the image, we can conclude that the other angle is 30 degrees because 180-90-60=30. After that, since 17 is the opposite side of 30 degrees and it is a 30-60-90 triangle, we multiply 17 by 1/sqrt(3) to get the side you're looking for to be 17/sqrt(3)= approximately 10 feet

Answer 2

The base of the tree should be staked at 9.815 feet.

Tangent (Tan θ)

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,  

$\rm{Tangent(\theta) = \dfrac{Perpendicular}{Base}$,

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

Given to us,

ropes tied on the tree trunk 17 feet above the ground, AB = 17 feet;

rope make a 60° angle with the ground, θ = 60°;

Base of the tree should be staked

$Tan (\theta) = \dfrac{tree\ trunk\ 17\ feet\ above\ the\ ground}{Distance\ between\ tree\ base}\\\\Tan (60^o) = \dfrac{AB}{BC}\\\\\sqrt{3} = \dfrac{17}{BC}\\\\BC = \dfrac{17}{\sqrt{3}}\\\\BC = 9.815$

Hence, the base of the tree should be staked at 9.815 feet.

Learn more about Tangent:

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