A tree needs to be staked down before a storm. If the ropes can be tied on the tree trunk 8 feet above the ground and the staked rope should make a 30 degree angle with the ground, how far, to the nearest tenth, from the base of the tree should each rope be staked?

Question

Mathematics

Belinda Hanna

2 August, 13:02

A tree needs to be staked down before a storm. If the ropes can be tied on the tree trunk 8 feet above the ground and the staked rope should make a 30 degree angle with the ground, how far, to the nearest tenth, from the base of the tree should each rope be staked?

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Answers (2)

Know the Answer?

Alec Buck · Answer 1

Refer to the diagram shown.

Let x = the distance from the base of three to where the rope is tied.

By definition,

tan 30° = 8/x

0.5774 = 8/x

Multiply each side by x.

0.5774x = 8

Divide each side by 0.5774

x = 13.855 ft

Answer: 13.9 ft (nearest tenth)

Braxton Ramos · Answer 2

divide the height * 8 feet) by the tangent of the opposite angle (30 degrees)

8 / tan (30) = 13.856

rounded to nearest tenth would be 13.9 feet