If the angle of elevation of top of a tower from a point on the ground which is `20sqrt(3)` m away from the foot of the tower is `30^(@)`, then find the height of the tower.

Answer

To find the height of the tower given the angle of elevation and the distance from the tower, we can follow these steps:

### Step 1: Understand the Problem
We have a tower (let's call it AB) and a point C on the ground that is `20√3` meters away from the foot of the tower (point B). The angle of elevation from point C to the top of the tower (point A) is `30°`. We need to find the height of the tower (AB).

### Step 2: Set Up the Right Triangle
In triangle ABC:
- AB is the height of the tower (h).
- BC is the distance from the foot of the tower to point C, which is `20√3` meters.
- Angle ACB is `30°`.

### Step 3: Use the Tangent Function
In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. Therefore, we can write:
\[ \tan(30°) = \frac{AB}{BC} \]
Substituting the known values:
\[ \tan(30°) = \frac{h}{20\sqrt{3}} \]

### Step 4: Substitute the Value of Tan(30°)
We know that:
\[ \tan(30°) = \frac{1}{\sqrt{3}} \]
So we can substitute this into the equation:
\[ \frac{1}{\sqrt{3}} = \frac{h}{20\sqrt{3}} \]

### Step 5: Cross-Multiply to Solve for h
Cross-multiplying gives us:
\[ h = 20\sqrt{3} \cdot \frac{1}{\sqrt{3}} \]
This simplifies to:
\[ h = 20 \text{ meters} \]

### Conclusion
The height of the tower is `20 meters`.

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