From a point on the ground 20m from the base of a tree the angle of the elevation to the top of the tree is 47 degrees. Calculate the height the of the tree correct to the nearest metre ???
To calculate the height of the tree, we can use trigonometry. The opposite side of the triangle formed by the tree and the ground is the height of the tree, and the adjacent side is the distance from the base of the tree.
1. Label the height of the tree as "h" and the distance from the base as "d."
2. From the information given, we know that the angle of elevation is 47 degrees and the distance from the base is 20m.
3. We can use the tangent function to calculate the height of the tree:
tan(angle) = opposite / adjacent
tan(47 degrees) = h / 20m
4. Rearrange the equation and solve for h:
h = 20m * tan(47 degrees)
5. Substitute the values into a calculator:
h = 20m * 0.989
h ≈ 19.78m
Therefore, the height of the tree is approximately 19.78 meters, rounded to the nearest meter.
To solve this problem, we will use the concept of trigonometry, specifically the tangent function.
Let's label the height of the tree as 'h'.
According to the problem, we have a right-angled triangle formed by the observer, the top of the tree, and the base of the tree. The observer is at a distance of 20 meters from the base of the tree.
The tangent of an angle in a right triangle can be defined as the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the tree, and the adjacent side is the distance from the observer to the base of the tree.
Using the tangent function, we have:
tan(angle) = opposite/adjacent
tan(47 degrees) = h/20
To find the height of the tree, we need to isolate the variable 'h'.
h = 20 * tan(47 degrees)
Now we can calculate the height using a scientific calculator or by looking up the value of the tangent of 47 degrees.
Plugging in the values, we find:
h ≈ 20 * 1.0724
h ≈ 21.448 meters
Rounding this value to the nearest meter, we get:
The height of the tree is approximately 21 meters.