A vertical pole of length 8 m casts a shadow 6 cm long on the ground and at the same time a tower casts a shadow 30 m long. Find the height of tower

Answer

To find the height of the tower using the information given about the vertical pole and its shadow, we can use the concept of similar triangles. Here’s a step-by-step solution:

### Step 1: Understand the problem
We have a vertical pole (BC) of height 8 m that casts a shadow (AB) of 6 cm. At the same time, a tower (EF) casts a shadow (DE) of 30 m. We need to find the height of the tower (EF).

### Step 2: Set up the triangles
We can denote:
- Height of the pole (BC) = 8 m
- Length of the shadow of the pole (AB) = 6 cm = 0.06 m (since we need to keep the units consistent)
- Length of the shadow of the tower (DE) = 30 m
- Height of the tower (EF) = h (unknown)

### Step 3: Use similar triangles
Since the sun casts shadows at the same angle, triangles ABC (pole and its shadow) and DEF (tower and its shadow) are similar. This gives us the following relationship based on the properties of similar triangles:

\[ \frac{AB}{DE} = \frac{BC}{EF} \]

### Step 4: Substitute the known values
Substituting the known values into the equation, we have:

\[ \frac{0.06}{30} = \frac{8}{h} \]

### Step 5: Cross-multiply to solve for h
Cross-multiplying gives us:

\[ 0.06 \cdot h = 8 \cdot 30 \]

Calculating the right side:

\[ 0.06h = 240 \]

### Step 6: Solve for h
Now, divide both sides by 0.06 to find h:

\[ h = \frac{240}{0.06} \]

Calculating this gives:

\[ h = 4000 \text{ m} \]

### Step 7: Conclusion
Thus, the height of the tower is **4000 m**.