From the top of a building 10m high, the angle of elevation of a fruit on top of a tree 25m is 30º. Calculate the horizontal distance between the building a...

Answer Details

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.