Question

Use the given measurements to solve each triangle.round to the nearest tenth please help

Answer 1

To find r, we have to use the law of cosines because the triangle is not right.

`\begin{gathered} r^2=9^2+7.5^2-2(9)(7.5)\cos 89 \\ r=\sqrt[]{81+56.25-2.36} \\ r\approx11.6 \end{gathered}`

Then, we find the angles using the law of sines.

`\begin{gathered} (PQ)/(\sin89)=(PR)/(\sin Q) \\ (11.6)/(\sin89)=(9)/(\sin Q) \end{gathered}`

Let's solve for Q.

`\begin{gathered} \sin Q=(9\cdot\sin 89)/(11.6)\approx0.78 \\ Q=\sin ^(-1)(0.78) \\ Q=51.3 \end{gathered}`

At last, we find the angle P using the interior angles theorem

`\begin{gathered} P+Q+R=180 \\ P+51.3+89=180 \\ P=180-89-51.3 \\ P=39.7 \end{gathered}`

Hence, r = 11.6, angle Q is 51.3°, and angle P is 39.7°.