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In triangle ABC, angle B = 90 degrees, AB = 8 cm and BC = 15 cm. Calculate the length of AC.

Mathematics

ScanSolve AI Answer

Answer

17 cm\text{17 cm}

Step-by-step solution

6 steps

  1. Identify the given information.

    We are given a right-angled triangle △ABC\triangle ABC, with the right angle at BB.
    The lengths of the two shorter sides are:
    AB=8 cmAB = 8 \text{ cm}
    BC=15 cmBC = 15 \text{ cm}
    We need to find the length of the hypotenuse, ACAC.

  2. Apply the Pythagorean theorem.

    For a right-angled triangle, the square of the hypotenuse (ACAC) is equal to the sum of the squares of the other two sides (ABAB and BCBC).

    AC2=AB2+BC2AC^2 = AB^2 + BC^2

  3. Substitute the given values into the formula.

    AC2=(8 cm)2+(15 cm)2AC^2 = (8 \text{ cm})^2 + (15 \text{ cm})^2

  4. Calculate the squares of the side lengths.

    AC2=64 cm2+225 cm2AC^2 = 64 \text{ cm}^2 + 225 \text{ cm}^2

  5. Add the squared values.

    AC2=289 cm2AC^2 = 289 \text{ cm}^2

  6. Take the square root of both sides to find ACAC.

    AC=289 cm2AC = \sqrt{289 \text{ cm}^2} AC=17 cmAC = 17 \text{ cm}

    The length of ACAC is 17 cm\boxed{\text{17 cm}}.

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