Final answer:
The height of the tree is 75 m, for a person on the bank of a river observes that the angle of elevation of the top of the tree standing on the opposite bank is 60 degrees. When he moves 50 m away from the bank, he finds the angle of elevation to be 30 degrees.
Step-by-step explanation:
Let's denote the height of the tree as x.
When the person is standing on the bank of the river, the angle of elevation to the top of the tree is 60 degrees.
This forms a right triangle, with the height of the tree as the opposite side and the distance to the tree as the adjacent side.
Therefore, in the first scenario, we can use the tangent function to find the height of the tree:
tan(60) = x/50
When the person moves 50 m away from the bank, the angle of elevation to the top of the tree becomes 30 degrees. Again, this forms a right triangle, with the height of the tree as the opposite side and the new distance to the tree as the adjacent side.
In the second scenario, we can use the tangent function again to find the height of the tree:
tan(30) = x/100
Solving these equations, we find that the height of the tree is 75 m.
Therefore, the correct answer is option c) The height of the tree is 75 m.