A TREE STANDS ON HORIZONTAL GROUND. THE ANGLE OF ELEVATION OF THE TOP OF THE TREE FROM A POINT 50 m AWAY FROM THE BASE OF THE TREE IS 11.3°. CALCULATE THE HEIGHT OF THE TREE.
Tan11.3 = h/50, h = ?.
Pls someone help me solving this question.
To calculate the height of the tree, we can use trigonometry and the given angle of elevation.
Let's break down the problem using a diagram:
|
| /|
| / | height (h)
| / |
| / |
| / |
| / |
| / |
| / |
| / |
|/ angle of elevation (11.3°)
|---------------------
distance (50 m)
In this scenario, we have formed a right triangle, where the base is the distance from the point to the tree (50 m), the height is the height of the tree (h), and the angle of elevation is the angle formed between the horizontal ground and the line of sight to the top of the tree.
We know that the tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
So, in this case, we have:
tan(angle of elevation) = height / distance
Plugging in the given values:
tan(11.3°) = h / 50
To find the height of the tree, we need to isolate 'h'. Rearranging the equation:
h = tan(11.3°) * 50
Calculating this expression will give us the height of the tree:
h ≈ tan(11.3°) * 50
Now, you can use a calculator or a trigonometric table to find the value of tan(11.3°). Multiply that by 50 to get the height of the tree in meters.