Question

the hypotenuse of a right triangle measures 10 cm and one of its legs measures 7 cm. find the measure of the other leg. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Let \(c = 10\) (hypotenuse) and \(a = 7\) (one leg). We want to find \(b\).

Step2: Substitute the values into the formula

We get \(7^{2}+b^{2}=10^{2}\).

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Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{51}\approx7.1\)

Answer:

\(7.1\) cm