A man 1.7m tall observe a bird on top of a tree at angle of elevation of 40degree. If the bird distance between the man's head and the bird is 25m, what is the height of the tree?
To find the height of the tree, we can use trigonometry. Let's call the height of the tree "x".
First, we need to determine the distance from the man's eyes to the bird's position on the tree. Since the bird is on top of the tree, we can assume that the distance from the man's eyes to the bird is equal to the distance from the man's head to the bird. Given that the distance is 25m, we will use this information in our calculations.
We have a right-angled triangle where the height of the tree (x) is the opposite side, the distance from the man's eyes to the bird (25m) is the adjacent side, and the angle of elevation (40 degrees) is the angle between the adjacent side and the hypotenuse.
In trigonometry, the tangent function (tan) relates the opposite and adjacent sides of a right triangle:
tan(angle) = opposite/adjacent
Therefore, we have:
tan(40 degrees) = x/25m
To find x, we need to isolate it. Rearranging the equation:
x = tan(40 degrees) * 25m
Using a scientific calculator:
x ≈ 0.8391 * 25m
x ≈ 20.978m
Hence, the height of the tree is approximately 20.978 meters.
the part of the tree above the man's eyes is h
h/25 = sin 40
h = 25sin40
tree is 1.7 + 25sin40 = 17.77
Of course, that assumes the man's eyes are on the top of his head. . .