Question

practice with the pythagorean theorem sp 26
find the value of ab. round to the nearest tenth.
4.7m
4.1m
ab=□

Explanation:

Step1: Recall Pythagorean Theorem

For right triangle $\triangle ABC$ (right-angled at $B$), the theorem states:
$$AB^2 + BC^2 = AC^2$$

Step2: Rearrange for $AB$

Isolate $AB^2$ by subtracting $BC^2$:
$$AB^2 = AC^2 - BC^2$$

Step3: Substitute given values

$AC=4.7\ \text{m}$, $BC=4.1\ \text{m}$:
$$AB^2 = (4.7)^2 - (4.1)^2 = 22.09 - 16.81 = 5.28$$

Step4: Calculate and round $AB$

Take square root and round to nearest tenth:
$$AB = \sqrt{5.28} \approx 2.3$$

Answer:

$2.3\ \text{m}$