Two poles 15 m and 30 m high stand upright in a play ground . If their feet be 36 m apart , find the distance between the tops.

Options

A. 41 m
B. 36 m
C. 39 m
D. none of these

Answer

To find the distance between the tops of two poles of heights 15 m and 30 m that are 36 m apart at their bases, we can use the Pythagorean theorem. Here’s a step-by-step solution:

### Step 1: Identify the heights of the poles
Let the height of the first pole (Pole A) be \( h_1 = 15 \) m and the height of the second pole (Pole B) be \( h_2 = 30 \) m.

### Step 2: Calculate the vertical distance between the tops of the poles
The vertical distance between the tops of the two poles is given by:
\[ \text{Vertical Distance} = h_2 - h_1 = 30 \, \text{m} - 15 \, \text{m} = 15 \, \text{m} \]

### Step 3: Identify the horizontal distance between the poles
The horizontal distance between the feet of the poles is given as \( d = 36 \) m.

### Step 4: Apply the Pythagorean theorem
To find the distance between the tops of the poles, we can treat this as a right triangle where:
- One leg is the vertical distance between the tops of the poles (15 m),
- The other leg is the horizontal distance between the poles (36 m).

According to the Pythagorean theorem:
\[ d^2 = a^2 + b^2 \]
where:
- \( d \) is the distance between the tops of the poles,
- \( a \) is the vertical distance (15 m),
- \( b \) is the horizontal distance (36 m).

Substituting the values:
\[ d^2 = (15)^2 + (36)^2 \]
\[ d^2 = 225 + 1296 \]
\[ d^2 = 1521 \]

### Step 5: Calculate the distance \( d \)
Now, take the square root to find \( d \):
\[ d = \sqrt{1521} = 39 \, \text{m} \]

### Conclusion
The distance between the tops of the two poles is \( 39 \) m.

---