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One of the legs of a right triangle measures 15cm and the other leg measures 9cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth. Answer: cm

One of the legs of a right triangle measures 15 cm 15 \mathrm{~cm} and the other leg measures 9 cm 9 \mathrm{~cm} .\newlineFind the measure of the hypotenuse. If necessary, round to the nearest tenth.\newlineAnswer: □\square cm \mathrm{cm}

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Full solution

Q. One of the legs of a right triangle measures 15 cm 15 \mathrm{~cm} and the other leg measures 9 cm 9 \mathrm{~cm} .\newlineFind the measure of the hypotenuse. If necessary, round to the nearest tenth.\newlineAnswer: □\square cm \mathrm{cm}
  1. Identify legs and formula: Identify the legs of the right triangle and the formula to use.\newlineWe have a right triangle with legs of 15 cm15\,\text{cm} and 9 cm9\,\text{cm}. We will use the Pythagorean Theorem to find the length of the hypotenuse, which states that in a right triangle, the square of the length of the hypotenuse (cc) is equal to the sum of the squares of the lengths of the other two sides (aa and bb).\newlineFormula: a2+b2=c2a^2 + b^2 = c^2
  2. Plug values into formula: Plug the known values into the Pythagorean Theorem.\newlineLet's denote the length of the hypotenuse as cc. We have:\newlinea=15a = 15 cm (one leg)\newlineb=9b = 9 cm (other leg)\newlinec=?c = ? (hypotenuse)\newlineNow, we plug the values into the formula:\newline152+92=c215^2 + 9^2 = c^2
  3. Calculate squares of legs: Calculate the squares of the legs.\newline152=22515^2 = 225\newline92=819^2 = 81\newlineNow, add these two values to find c2c^2:\newline225+81=c2225 + 81 = c^2
  4. Add results for c2c^2: Add the results to find c2c^2.225+81=306225 + 81 = 306So, c2=306c^2 = 306
  5. Take square root of c2c^2: Take the square root of c2c^2 to find the length of the hypotenuse.c=306c = \sqrt{306}Using a calculator, we find that:c≈17.5c \approx 17.5
  6. Round to nearest tenth: Round the result to the nearest tenth, if necessary.\newlineThe square root of 306306 is approximately 17.517.5, which is already to the nearest tenth.

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