the hypotenuse of a right triangle measures 10 cm and one of its legs measures 7 cm. find the measure of the…

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}). [ \begin{align*} 49 + b^{2}&=100\ b^{2}&=100 - 49\ b^{2}&=51 \end{align*} ]

Step3: Solve for (b)

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

Answer:

(7.1) cm