Final answer:
Using the tangent function and substituting the given values, the height of the tree is approximately 5.77 meters.
Step-by-step explanation:
To find the height of the tree, we can use trigonometry. Let's define the following: h = height of the tree, d = distance from the foot of the tree to the point where the tree touched the ground, and θ = angle between the ground and the broken upper part of the tree. We are given that d = 10 meters and θ = 30 degrees.
Using the tangent function, we can set up the equation:
tan(θ) = h/d
Substituting the given values:
tan(30) = h/10
solve for h:
h = tan(30) * 10
Using a calculator, we find that h ≈ 5.77 meters.