A girl is standing 6m at thesame level with a tree of 8m . Calculate the distance from the top of the tree to where the girl is standing. What is the angle of elevation of the tree from where the girl is standing

To calculate the distance from the top of the tree to where the girl is standing, we can use the Pythagorean theorem.

If the girl is standing 6m away from the tree, and the tree is 8m tall, then the distance from the top of the tree to where the girl is standing can be found using the equation:

distance^2 = (girl's distance from the tree)^2 + (tree's height)^2

distance^2 = 6^2 + 8^2
distance^2 = 36 + 64
distance^2 = 100
distance = √100
distance = 10m

Therefore, the distance from the top of the tree to where the girl is standing is 10m.

To find the angle of elevation of the tree from where the girl is standing, we can use the inverse tangent function. The angle of elevation is the angle between the horizontal line from where the girl is standing and the line of sight to the top of the tree.

angle = arctan(tree's height / girl's distance from the tree)
angle = arctan(8/6)

Using a calculator, we find that the angle of elevation is approximately 53.13 degrees.

Therefore, the angle of elevation of the tree from where the girl is standing is approximately 53.13 degrees.

To calculate the distance from the top of the tree to where the girl is standing, we can use the concept of similarity of triangles.

Let's consider the triangle formed by the girl, the base of the tree, and the top of the tree. The height of the tree is 8m, and the distance of the girl from the base of the tree is 6m.

Since the girl is at the same level as the base of the tree, the top of the tree, the girl, and the base of the tree form a right-angled triangle.

Using the concept of similar triangles, we can establish the following relationship:

(height of the tree) / (distance from the base to the girl) = (height of the triangle) / (distance from the top to the girl)

Substituting the values we know:
8m / 6m = (height of the triangle) / (distance from the top to the girl)

Simplifying this equation, we find:
4/3 = (height of the triangle) / (distance from the top to the girl)

To find the distance from the top of the tree to where the girl is standing, we need to solve for the height of the triangle. Rearranging the equation:

(height of the triangle) = (4/3) * (distance from the top to the girl)

Now, let's calculate the height of the triangle:
(height of the triangle) = (4/3) * 6m = 24/3 = 8m

Therefore, the distance from the top of the tree to where the girl is standing is 8m.

To calculate the angle of elevation of the tree from where the girl is standing, we can use trigonometry. The angle of elevation is the angle between the line of sight from the girl to the top of the tree and the horizontal level.

Considering the right-angled triangle formed by the girl, the base of the tree, and the top of the tree, we can use the inverse tangent function (arctan) to find the angle:

Angle of elevation = arctan(height of the tree / distance from the girl to the base of the tree)

Angle of elevation = arctan(8m / 6m)

Using a calculator or trigonometric tables, we find that arctan(8/6) is approximately 53.13 degrees.

Therefore, the angle of elevation of the tree from where the girl is standing is approximately 53.13 degrees.

Ans@=90