Question

what is the length of the hypotenuse? if necessary, round to the nearest tenth. c = \square centimeters

Explanation:

Step1: Identify the formula

For a right - triangle, we use the Pythagorean theorem, which is \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse. Here, \(a = 70\) cm and \(b=24\) cm.

Step2: Substitute the values into the formula

Substitute \(a = 70\) and \(b = 24\) into the formula: \(c^{2}=70^{2}+24^{2}\). Calculate \(70^{2}=4900\) and \(24^{2} = 576\). Then \(c^{2}=4900 + 576=5476\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{5476}\). We know that \(\sqrt{5476}=74\) (since \(74\times74 = 5476\)).

Answer:

74