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A triangle has side lengths =8m,sqrt15m,7m A) Is the triangle a right triangle? (type yes or no in the blank) qquad B) Give the number proof for your answer in "A" here qquad

A triangle has side lengths =8 m,15 m,7 m =8 \mathrm{~m}, \sqrt{15} \mathrm{~m}, 7 \mathrm{~m} \newlineA) Is the triangle a right triangle? (type yes or no in the blank) \qquad \newlineB) Give the number proof for your answer in

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Q. A triangle has side lengths =8 m,15 m,7 m =8 \mathrm{~m}, \sqrt{15} \mathrm{~m}, 7 \mathrm{~m} \newlineA) Is the triangle a right triangle? (type yes or no in the blank) \qquad \newlineB) Give the number proof for your answer in
  1. Use Pythagorean Theorem: To check if the triangle is a right triangle, use the Pythagorean theorem, which states that in a right 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. That is, if cc is the length of the hypotenuse and aa and bb are the lengths of the other two sides, the Pythagorean theorem can be written as c2=a2+b2c^2 = a^2 + b^2.
  2. Calculate Squares of Sides: Assume the longest side, 8 m8\,\text{m}, is the hypotenuse. Calculate the squares of the other two sides: (15)2=15(\sqrt{15})^2 = 15 and 72=497^2 = 49.
  3. Add Squares of Sides: Add the squares of the two shorter sides: 15+49=6415 + 49 = 64.
  4. Compare Sum of Squares: Compare the sum of the squares of the two shorter sides to the square of the longest side: 64=8264 = 8^2.
  5. Confirm Right Triangle: Since the sum of the squares of the two shorter sides equals the square of the longest side, the triangle is a right triangle.

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