In `triangleABC` right angled at C. AB= 1.7 cm, BC= 1.5 cm, find CA

Answer

To solve the problem, we will use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
- In triangle ABC, we know that it is right-angled at C.
- The hypotenuse is AB, and the other two sides are BC and CA.
- Given: AB = 1.7 cm, BC = 1.5 cm.

2. **Apply the Pythagorean theorem**:
- According to the theorem:
\[ AB^2 = AC^2 + BC^2 \]
- Substituting the known values:
\[ (1.7)^2 = AC^2 + (1.5)^2 \]

3. **Calculate the squares**:
- Calculate \(AB^2\):
\[ (1.7)^2 = 2.89 \]
- Calculate \(BC^2\):
\[ (1.5)^2 = 2.25 \]

4. **Set up the equation**:
- Now we can substitute these values into the equation:
\[ 2.89 = AC^2 + 2.25 \]

5. **Isolate \(AC^2\)**:
- Rearranging the equation to find \(AC^2\):
\[ AC^2 = 2.89 - 2.25 \]

6. **Perform the subtraction**:
- Calculate:
\[ AC^2 = 0.64 \]

7. **Find \(AC\)**:
- To find \(AC\), take the square root of both sides:
\[ AC = \sqrt{0.64} = 0.8 \text{ cm} \]

### Final Answer:
The length of side CA is \(0.8 \text{ cm}\).

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