Question

one of the legs of a right triangle measures 18 cm and the other leg measures 5 cm. find the measure of the hypotenuse. if necessary, round to the nearest tenth.

Explanation:

Step1: Recall Pythagorean theorem

The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $a$ and $b$ are the legs of the right - triangle and $c$ is the hypotenuse. Let $a = 18$ cm and $b = 5$ cm.

Step2: Substitute values into the formula

Substitute $a = 18$ and $b = 5$ into $a^{2}+b^{2}=c^{2}$, we get $18^{2}+5^{2}=c^{2}$. Calculate $18^{2}=18\times18 = 324$ and $5^{2}=5\times5 = 25$. Then $324 + 25=c^{2}$, so $c^{2}=349$.

Step3: Solve for $c$

Take the square root of both sides: $c=\sqrt{349}\approx18.7$ cm.

Answer:

$18.7$ cm