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One of the legs of a right triangle measures 3cm and the other leg measures 4cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth. Answer: cm

One of the legs of a right triangle measures 3 cm 3 \mathrm{~cm} and the other leg measures 4 cm 4 \mathrm{~cm} . Find 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 3 cm 3 \mathrm{~cm} and the other leg measures 4 cm 4 \mathrm{~cm} . Find the measure of the hypotenuse. If necessary, round to the nearest tenth.\newlineAnswer: □\square cm \mathrm{cm}
  1. Identify legs and relationship: Identify the legs of the right triangle and the relationship between the legs and the hypotenuse.\newlineThe legs of the right triangle are given as 3 cm3\,\text{cm} and 4 cm4\,\text{cm}. According to the Pythagorean theorem, the square of the hypotenuse (cc) is equal to the sum of the squares of the other two sides (aa and bb).\newlineMathematically, this is represented as a2+b2=c2a^2 + b^2 = c^2.
  2. Substitute values into theorem: Substitute the given values into the Pythagorean theorem.\newlineWe have a=3 cma = 3\, \text{cm} and b=4 cmb = 4\, \text{cm}. Plugging these values into the equation, we get:\newline32+42=c23^2 + 4^2 = c^2.
  3. Calculate squares of measurements: Calculate the squares of the given leg measurements.\newline32=93^2 = 9 and 42=164^2 = 16. Adding these together gives us:\newline9+16=c29 + 16 = c^2.
  4. Add results for hypotenuse: Add the results to find the square of the hypotenuse. 9+16=259 + 16 = 25. So, c2=25c^2 = 25.
  5. Take square root to solve: Take the square root of both sides of the equation to solve for cc.c2=25\sqrt{c^2} = \sqrt{25}, which simplifies to c=5c = 5.
  6. Check result for confirmation: Check the result to ensure it makes sense in the context of the problem.\newlineSince 33 and 44 are the lengths of the legs of a well-known Pythagorean triple (3,4,5)(3, 4, 5), the hypotenuse should indeed be 55 cm. This confirms that our calculation is correct.

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