Final answer:
Using trigonometry, the wire is found to be attached to the tree at a height of approximately 8.746 meters above the ground.
Step-by-step explanation:
To find the height at which a wire is attached to a tree, given that the wire is 10.0 m long and makes an angle of 61 degrees with the ground, we can use trigonometry. In this scenario, we have a right triangle where the wire represents the hypotenuse, the height of the tree represents the opposite side, and the ground represents the adjacent side. We can use the sine function which is defined as the ratio of the opposite side to the hypotenuse.
So, the height (h) can be calculated as follows:
sin(61°) = h / 10.0 mh = sin(61°) × 10.0 mh = 0.8746 × 10.0 mh = 8.746 m
The wire is therefore attached to the tree at a height of approximately 8.746 meters above the ground.