Question

question
one of the legs of a right triangle measures 1 cm and its hypotenuse measures 17 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Let one leg \(a = 1\), hypotenuse \(c = 17\), and the other leg be \(b\). We need to solve for \(b\). Rearranging the formula: \(b=\sqrt{c^{2}-a^{2}}\)

Step2: Substitute values

Substitute \(a = 1\) and \(c = 17\) into the formula: \(b=\sqrt{17^{2}-1^{2}}\)

Step3: Calculate the values inside the square root

First, calculate \(17^{2}=289\) and \(1^{2}=1\). Then \(17^{2}-1^{2}=289 - 1=288\)

Step4: Simplify the square root

\(b=\sqrt{288}\). We can simplify \(\sqrt{288}=\sqrt{144\times2}=12\sqrt{2}\approx12\times1.414 = 16.968\)

Step5: Round to the nearest tenth

Rounding \(16.968\) to the nearest tenth gives \(17.0\) (since the hundredth digit is 6, which is more than 5, we round up the tenth digit 9 to 10, carrying over to the ones place, so 16.968 ≈ 17.0 when rounded to the nearest tenth)

Answer:

The measure of the other leg is \(\boldsymbol{17.0}\) cm (or approximately 17.0 cm).