A vertical stick 12 m long casts a shadow 8 m long on the ground. At the same time, a tower casts a shadow of 40 m long on the ground. The height of the tower is

Options

A. 60 m
B. 65 m
C. 70 m
D. 72 m

Answer

To solve the problem, we will use the concept of similar triangles. The height of the stick and its shadow form one triangle, while the height of the tower and its shadow form another triangle. Since both triangles are similar, we can set up a proportion to find the height of the tower.

### Step-by-Step Solution:

1. **Identify the given values:**
- Height of the stick (h1) = 12 m
- Length of the shadow of the stick (s1) = 8 m
- Length of the shadow of the tower (s2) = 40 m
- Height of the tower (h2) = ?

2. **Set up the proportion using similar triangles:**
Since the triangles are similar, we can write the proportion:
\[ \frac{h1}{s1} = \frac{h2}{s2} \]
Substituting the known values:
\[ \frac{12}{8} = \frac{h2}{40} \]

3. **Cross-multiply to solve for h2:**
\[ 12 \times 40 = 8 \times h2 \]
\[ 480 = 8 \times h2 \]

4. **Divide both sides by 8 to isolate h2:**
\[ h2 = \frac{480}{8} \]
\[ h2 = 60 \]

5. **Conclusion:**
The height of the tower is 60 meters.

### Final Answer:
The height of the tower is **60 meters**.

---