A vertical pole of length 6 m casts a shadow 4 m long on the ground at the same time a tower casts a shadow 28 m long what is the height of the tower?

Options

A. 45 cm
B. 36 cm
C. 42 cm
D. 64 cm

Answer

To find the height of the tower based on the given information, 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 of height 6 m that casts a shadow of 4 m. At the same time, a tower casts a shadow of 28 m. We need to find the height of the tower.

### Step 2: Set Up the Ratios
Since the sun’s rays create similar triangles, we can set up the following ratio based on the heights and shadows:

\[ \frac{\text{Height of Pole}}{\text{Length of Pole's Shadow}} = \frac{\text{Height of Tower}}{\text{Length of Tower's Shadow}} \]

Substituting the known values:

\[ \frac{6 \text{ m}}{4 \text{ m}} = \frac{h}{28 \text{ m}} \]

where \( h \) is the height of the tower.

### Step 3: Cross-Multiply to Solve for \( h \)
Cross-multiplying gives us:

\[ 6 \text{ m} \times 28 \text{ m} = 4 \text{ m} \times h \]

Calculating the left side:

\[ 168 \text{ m}^2 = 4 \text{ m} \times h \]

### Step 4: Isolate \( h \)
Now, divide both sides by 4 m to solve for \( h \):

\[ h = \frac{168 \text{ m}^2}{4 \text{ m}} = 42 \text{ m} \]

### Conclusion
The height of the tower is \( 42 \text{ m} \).

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