Question

The trunk of a leaning tree makes an angle of 12° with the vertical. To prevent the tree from falling, a 35 m rope is attached to the top of the tree and pegged into the ground some distance away (assume the ground is level). If the tree is 20 m tall, what angle does the rope make with the ground?

K: 1, T: 1, C: 1, A: 1

Answer 1

The angle the rope makes with the ground is approximately 34.85 degrees.

The situation form a right angle triangle.

Therefore, the 35 meters rope attached to the top of tree to the ground is the hypotenuse of the triangle.

The height of the tree is the opposite side of the triangle.

Therefore, using trigonometric ratios we can find the angle the rope make with the ground.

let

∅ = angle the rope make with the ground

sin ∅ = opposite / hypotenuse

sin ∅ = 20 / 35

∅ = sin⁻¹ 0.57142857142

∅ = 34.849904579

∅ = 34.85°

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