Final answer:
The tree is broken 6 meters above the ground. This was determined using the cosine of a 60° angle in a right-angled triangle formed by the broken tree.
Step-by-step explanation:
The question 'At what height from the bottom, the tree is broken by the wind?' pertains to a problem involving a right-angled triangle, with the tree forming the hypotenuse and the ground level forming the base when the tree touches the ground at a 60° angle. To solve for the height at which the tree broke (the opposite side of the 60° angle), we can use trigonometry. The height (opposite side) can be calculated using the cosine of the angle, given by the relationship (cos 60° = adjacent/hypotenuse).
Let's denote the height from the bottom where the tree is broken as 'h'. The part of the tree touching the ground is then given by (12 - h). Since the hypotenuse (the original length of the tree) is 12 m, we can use the following equation based on the cosine relationship: cos 60° = (12 - h) / 12.
The cosine of 60° is 0.5, so the equation simplifies to 0.5 = (12 - h) / 12. Solving for 'h', we get h = 12 - (0.5 × 12) = 12 - 6 = 6 m. This means that the tree is broken by the wind 6 m above the ground.