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Calculate the value of AC

September 26, 2026Mathematics

ScanSolve AI Answer

Answer

17 \text{ cm}

6 steps

To calculate the value of AC, we will use the Pythagorean theorem, as $\triangle ABC$ is a right-angled triangle with $\angle B = 90^\circ$ .

Identify the given side lengths.
We are given:
$AB = 8 \text{ cm}$
$BC = 15 \text{ cm}$
Apply the Pythagorean theorem.
The Pythagorean theorem states that $AC^2 = AB^2 + BC^2$ .
Substitute the given values into the formula.
$AC^2 = (8 \text{ cm})^2 + (15 \text{ cm})^2$
Calculate the squares of the side lengths.
$AC^2 = 64 \text{ cm}^2 + 225 \text{ cm}^2$
Add the squared values.
$AC^2 = 289 \text{ cm}^2$
Take the square root to find the length of AC.
$AC = \sqrt{289 \text{ cm}^2}$ $AC = \boxed{17 \text{ cm}}$

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