To find the horizontal distance between the building and the tree, we need to use some basic trigonometry. Let's break it down step by step in a simple manner.
Step 1: Identify the right triangle.
We are dealing with a scenario where the top of the building, the top of the tree, and the ground form a right triangle. In this triangle:
- The height difference between the top of the tree and the building is the opposite side.
- The horizontal distance (which we need to find) is the adjacent side.
- The angle of elevation is 30º.
Step 2: Calculate the height difference (opposite side).
The tree's height is 25 meters, and the building's height is 10 meters, so the height difference is:
Opposite side = 25m - 10m = 15m
Step 3: Use the tangent function.
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. Thus:
tan(30º) = Opposite / Adjacent
tan(30º) = 15 / D, where D is the horizontal distance we need to find.
Step 4: Solve for the horizontal distance.
The tangent of 30 degrees is 1/√3. Therefore:
(1/√3) = 15 / D
To solve for D, multiply both sides by D and multiply by √3:
D = 15 * √3
The horizontal distance between the building and the tree is 15√3 meters.