In Delta PQR,r=38cm,mangle P=49^circ and mangle Q=127^circ Find the length of p.to the nearest centimeter. Answer Attemptiout of 2 p=square cm

We are given a triangle PQR with $r=38$ cm, $m\angle P = 49^\circ$, and $m\angle Q = 127^\circ$. We want to find the length of side $p$.<br /><br />We can use the Law of Sines to solve for $p$. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant. That is:<br /><br />$\frac{p}{\sin P} = \frac{q}{\sin Q} = \frac{r}{\sin R}$<br /><br />We are given $r$ and $\angle P$, and we can find $\angle R$ since the sum of the angles in a triangle is $180^\circ$:<br /><br />$m\angle R = 180^\circ - m\angle P - m\angle Q = 180^\circ - 49^\circ - 127^\circ = 180^\circ - 176^\circ = 4^\circ$<br /><br />Now we can use the Law of Sines with $r$, $\angle R$, and $\angle P$ to find $p$:<br /><br />$\frac{p}{\sin P} = \frac{r}{\sin R}$<br /><br />$p = \frac{r \sin P}{\sin R}$<br /><br />$p = \frac{38 \sin 49^\circ}{\sin 4^\circ}$<br /><br />$p = \frac{38 \times 0.7547}{0.0698}$<br /><br />$p \approx \frac{28.6786}{0.0698}$<br /><br />$p \approx 410.87$<br /><br />So, the length of side $p$ is approximately 411 cm.<br /><br />Final Answer: The final answer is $\boxed{411}$<br />