A triangular field ABC, right angled at A has length `AC=33m` and `AB=180m`. The length of the side BC is

Options

A. 193 m
B. 189 m
C. 188 m
D. 183 m

Answer

To find the length of side BC in the right-angled triangle ABC, where the right angle is at A, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (BC in this case) is equal to the sum of the squares of the lengths of the other two sides (AC and AB).

### Step-by-Step Solution:

1. **Identify the sides of the triangle:**
- AC = 33 m (one leg)
- AB = 180 m (the other leg)
- BC = ? (hypotenuse)

2. **Apply the Pythagorean theorem:**
\[ BC^2 = AB^2 + AC^2 \]

3. **Substitute the known values:**
\[ BC^2 = (180)^2 + (33)^2 \]

4. **Calculate the squares:**
\[ BC^2 = 32400 + 1089 \]

5. **Add the results:**
\[ BC^2 = 33489 \]

6. **Take the square root to find BC:**
\[ BC = \sqrt{33489} \]

7. **Calculate the square root:**
- We can simplify \( \sqrt{33489} \) by checking for perfect squares.
- We find that \( 61^2 = 3721 \), thus:
\[ 33489 = 3^2 \times 61^2 \]
- Therefore:
\[ BC = 3 \times 61 = 183 \text{ m} \]

### Final Answer:
The length of side BC is **183 meters**.