Question

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?

Answer 1

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

Answer 2

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)