Question

22 multiple choice 2 points if the lengths of the legs of a right triangle are 5 and 12, what is the length of the hypotenuse? 17 13 $sqrt{17}$ $sqrt{119}$ 23 multiple choice 2 points what is the measure of angle r? 39° 29° 17° 31°

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with leg lengths \(a\) and \(b\) and hypotenuse length \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 5\) and \(b=12\).
\[c^{2}=5^{2}+12^{2}\]

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

\[5^{2}=25\], \[12^{2}=144\], then \(c^{2}=25 + 144=169\).

Step3: Find \(c\)

Take the square - root of both sides. Since \(c>0\), \(c=\sqrt{169}=13\).

Step1: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is \(180^{\circ}\). In \(\triangle RQS\), we know \(\angle Q = 92^{\circ}\) and \(\angle S=59^{\circ}\), and we want to find \(\angle R\). Let \(\angle R=x\). Then \(x + 92^{\circ}+59^{\circ}=180^{\circ}\).

Step2: Solve for \(x\)

\[x=180^{\circ}-(92^{\circ}+59^{\circ})=180^{\circ}-151^{\circ}=29^{\circ}\]

Answer:

B. 13