The angle of elevation of the top of a lower at a distance of 25 m from its foot is `60^(@)` The approximate height of the tower is -

Options

A. 20.3 m
B. 15.3 m
C. 36.3 m
D. 43.3 m

Answer

To find the approximate height of the tower given the angle of elevation and the distance from the foot of the tower, we can use trigonometric ratios. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have a tower, and we need to find its height (let's denote it as \( h \)). We know the distance from the foot of the tower to the point of observation is 25 m, and the angle of elevation from that point to the top of the tower is \( 60^\circ \).

### Step 2: Set Up the Right Triangle
We can visualize this situation as a right triangle where:
- The height of the tower is the opposite side (\( h \)).
- The distance from the foot of the tower to the observation point is the adjacent side (25 m).
- The angle of elevation is \( 60^\circ \).

### Step 3: Use the Tangent Function
The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. Thus, we can write:
\[ \tan(60^\circ) = \frac{h}{25} \]

### Step 4: Find the Value of \( \tan(60^\circ) \)
From trigonometric tables or a calculator, we know:
\[ \tan(60^\circ) = \sqrt{3} \approx 1.732 \]

### Step 5: Substitute and Solve for \( h \)
Substituting the value of \( \tan(60^\circ) \) into the equation gives:
\[ \sqrt{3} = \frac{h}{25} \]
Now, we can solve for \( h \):
\[ h = 25 \times \sqrt{3} \]

### Step 6: Calculate \( h \)
Using the approximate value of \( \sqrt{3} \approx 1.732 \):
\[ h = 25 \times 1.732 \approx 43.3 \text{ m} \]

### Conclusion
The approximate height of the tower is \( 43.3 \) meters.