Question

question find the measure of $overline{jk}$. answer attempt 1 out of 2

Explanation:

Step1: Apply the Law of Cosines

The Law of Cosines for finding the side length \(c\) in a triangle with sides \(a\), \(b\) and the included - angle \(C\) is \(c^{2}=a^{2}+b^{2}-2ab\cos C\). In \(\triangle IJK\), let \(a = 19\), \(b = 32\), and assume the included - angle between them is \(C\). If we want to find the length of \(JK\) (let \(JK = c\)), we have \(c^{2}=19^{2}+32^{2}-2\times19\times32\times\cos C\). However, if the angle between the two given sides is \(90^{\circ}\) (not shown in the problem but if it is a right - triangle situation), we can use the Pythagorean theorem. Since \(19\) and \(32\) are the two legs of a right - triangle, by the Pythagorean theorem \(c=\sqrt{a^{2}+b^{2}}\), where \(a = 19\) and \(b = 32\).

Step2: Calculate the value

\[

$$\begin{align*} c&=\sqrt{19^{2}+32^{2}}\\ &=\sqrt{361 + 1024}\\ &=\sqrt{1385}\\ &\approx37.2 \end{align*}$$

\]

Answer:

\(\sqrt{1385}\approx37.2\)