Question

semester a
what is the length of the hypotenuse of the triangle?
$\sqrt{161}$ cm
$\sqrt{94}$ cm
23 cm
17 cm

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle \(ABC\) with legs \(a = 8\) ( \(AC\) ) and \(b = 15\) ( \(BC\) ), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\), where \(c\) is the hypotenuse (\(AB\)).
So, \(c^{2}=8^{2}+15^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(8^{2}=64\) and \(15^{2}=225\). Then \(a^{2}+b^{2}=64 + 225=289\).

Step3: Find \(c\)

Since \(c^{2}=289\), then \(c=\sqrt{289}\). And \(\sqrt{289}=17\) (because \(17\times17 = 289\)).

Answer:

\(17\space cm\)