In a `/_\ ABC`, if `/_A = 90^(@)`, then `BC^(2)` = (.....) + (.....).

Answer

To solve the problem, we need to apply the Pythagorean theorem to triangle ABC, where angle A is 90 degrees. Here's the step-by-step solution:

### Step 1: Identify the triangle and its sides
In triangle ABC, we know:
- Angle A = 90 degrees (right angle)
- Side AB is perpendicular to side AC
- Side BC is the hypotenuse of the triangle

### Step 2: Apply the Pythagorean theorem
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (BC) is equal to the sum of the squares of the lengths of the other two sides (AB and AC). Mathematically, this is expressed as:
\[ BC^2 = AB^2 + AC^2 \]

### Step 3: Write the final expression
From the application of the Pythagorean theorem, we can conclude:
\[ BC^2 = AB^2 + AC^2 \]

### Step 4: Fill in the blanks
Thus, we can fill in the blanks in the given statement:
\[ BC^2 = AB^2 + AC^2 \]

### Final Answer:
BC² = AB² + AC²

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