A man whose eye is 120 m above the ground is standing 8 m from a 7 m tall.What is the angle of elevation of the top of the tree from its eye?
A man whose eye is 120cm above the ground is standing 8m from a tree 7m tall what is the angle of elevation of the top of the tree
ever proofread what you write?
Ever see a 120m tall man?
I'll assume his eye is 1.2m up (quite a short man). Then
tanθ = (7-1.2)/8
Maybe you can fix up whatever numbers you have botched.
40
Well, well, well, looks like we have a tree-mendous problem here! Let's branch out and solve it with a sprinkle of humor, shall we?
To find the angle of elevation, we need to consider the height of the tree, the distance to the tree, and the height of the man's eye. So, let's get calculating!
We can form a right-angled triangle using the man's eye, the top of the tree, and the point where the man is standing. The height of the tree is 7 meters, and the man's eye is 120 meters above the ground. The distance between the man and the tree is 8 meters.
Now, if we imagine drawing two lines from the bottom of the tree to the man's eye and from the bottom of the tree to the point where the man is standing, we have ourselves a right-angled triangle.
The vertical side of this triangle has a length of 7 meters (the height of the tree), and the hypotenuse (the line connecting the man's eye to the top of the tree) has a length of 120 meters.
To find the angle of elevation, we can use the lovely tangent function. Tangent(angle) = Opposite(side) / Adjacent(side). In our case, the opposite side is 7 meters, and the adjacent side is 120 - 8 = 112 meters.
So, the angle of elevation can be calculated as tan(angle) = 7 / 112. And if we take the inverse tangent (or arctan) of that, we'll get our answer.
Now, let me just do a little magic with my calculator here... *poof*
And voila! The angle of elevation of the top of the tree from the man's eye is approximately 3.56 degrees.
Hope that gave you a good laugh, and remember, there's always a silly way to solve every problem!
To find the angle of elevation of the top of the tree from the man's eye, we can use trigonometry. The angle of elevation is the angle between the line of sight from the eye to the top of the tree and the horizontal ground.
Let's label the points involved:
A: The man's eye
B: The top of the tree
C: The base of the tree (where the man is standing)
We are given that the height of the man's eye above the ground is 120 m, and the height of the tree is 7 m. The distance from the man to the base of the tree is 8 m.
Using the given information, we can draw a right triangle ABC, where AB is the line of sight from the man's eye to the top of the tree, and BC is the height of the tree.
Now, we want to find the angle of elevation, which is the angle BAC.
We can use the tangent function to find this angle:
tan(BAC) = opposite/adjacent
In this case, the opposite side is the height of the tree (BC = 7 m), and the adjacent side is the distance from the man to the base of the tree (AC = 8 m).
tan(BAC) = 7/8
Now, we can find the angle BAC by taking the inverse tangent (arctan) of both sides:
BAC = arctan(7/8)
Using a scientific calculator or an online trigonometry calculator, we can find the angle BAC.
So, the angle of elevation of the top of the tree from the man's eye is approximately equal to arctan(7/8).