Answer Key 11.8
[latexpage]
- \(\begin{array}{rrl}
\\ \\ \\ \\
z^2&=&10^2+20^2-2(10)(20)\text{ cos }40^{\circ} \\
z^2&=&100+400-306.4 \\
z^2&=&193.6 \\ \\
z&=&13.9\text{ cm}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\
20^2&=&28^2+28^2-2(28)(28)\text{ cos }{\O} \\ \\
400&=&784+784-1568\text{ cos }{\O} \\ \\
\text{cos }{\O}&=&\dfrac{-1168}{-1568} \\ \\
{\O}&=&\text{cos}^{-1}0.7449 \\ \\
{\O}&=&41.8^{\circ}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\
140^2&=&200^2+130^2-2(200)(130)\text{ cos }{\O} \\ \\
19600&=&400000+169000-52000\text{ cos }{\O} \\ \\
\text{cos }{\O}&=&\dfrac{-37300}{-52000} \\ \\
{\O}&=&\text{cos}^{-1}0.71730 \\ \\
{\O}&=&44.2^{\circ}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\
x^2&=&125^2+120^2-2(125)(120)\text{ cos }32^{\circ} \\
x^2&= &15625+14400-25441 \\
x^2&=&4583.6 \\
x&=&67.7
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
18^2&=&3^2+20^2-2(3)(20)\text{ cos }{\O} \\ \\
324&=&9+400-120\text{ cos }{\O} \\ \\
\text{cos }{\O}&=&\dfrac{-85}{-120} \\ \\
{\O}&=&\text{cos}^{-1}\left(\dfrac{-85}{-120}\right) \\ \\
{\O}&=&44.9^{\circ}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\
\dfrac{y}{\text{sin }35^{\circ}}&=&\dfrac{40}{\text{sin }65^{\circ}} \\ \\
y&=&\dfrac{40\text{ sin }35^{\circ}}{\text{sin }65^{\circ}} \\ \\
y&=&25.3
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\
\dfrac{y}{\text{sin }28^{\circ}}&=&\dfrac{12\text{ m}}{\text{sin }25^{\circ}} \\ \\
y&=&\dfrac{12\text{ sin }28^{\circ}}{\text{sin }25^{\circ}} \\ \\
y&=&13.3\text{ m}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\
\dfrac{x}{\text{sin }25^{\circ}}&=&\dfrac{10\text{ m}}{\text{sin }15^{\circ}} \\ \\
x&=&\dfrac{10\text{ m sin }25^{\circ}}{\text{sin }15^{\circ}} \\ \\
x&=&16.3\text{ m}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\
\dfrac{z}{\text{sin }10^{\circ}}&=&\dfrac{8\text{ cm}}{\text{sin }70^{\circ}} \\ \\
z&=&\dfrac{8\text{ cm sin }10^{\circ}}{\text{sin }70^{\circ}} \\ \\
z&=&1.48\text{ cm}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\
y^2&=&20^2+28^2-2(20)(28)\text{ cos }130^{\circ} \\
y^2&=&400+784+720 \\
y^2&=&1904 \\ \\
y&=&43.6\text{ cm}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
20^2&=&15^2+30^2-2(15)(30)\text{ cos }{\O} \\ \\
400&=&225+900-900\text{ cos }{\O} \\ \\
\text{ cos }{\O}&=&\dfrac{-725}{-900} \\ \\
{\O}&=&\text{cos}^{-1}\left(\dfrac{-725}{-900}\right) \\ \\
{\O}&=&36.3^{\circ}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\
\dfrac{x}{\text{sin }95^{\circ}}&=&\dfrac{8\text{ m}}{\text{sin }20^{\circ}} \\ \\
x&=&\dfrac{8\text{ m sin }95^{\circ}}{\text{sin }20^{\circ}} \\ \\
x&=&23.3
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\
16^2&=&10^2+8^2-2(8)(10)\text{ cos}{\O} \\ \\
256&=&100+64-160\text{ cos }{\O} \\ \\
\text{ cos }{\O}&=&\dfrac{92}{-160} \\ \\
{\O}&=&\text{ cos }^{-1}-0.575 \\ \\
{\O}&=&125^{\circ}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\
y^2&=&20^2+24^2-2(20)(24)\text{ cos }15^{\circ} \\
y^2&=&400+576-960\text{ cos }15^{\circ} \\
y^2&=&976-927.3 \\
y&=&\sqrt{48.7} \\ \\
y&=&6.98\text{ cm}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\ \\ \\ \\ \\ \\
20^2&=&10^2+22^2-2(10)(22)\text{ cos }{\O} \\ \\
400&=&100+484-440\text{ cos }{\O} \\ \\
\text{ cos }{\O}&=&\dfrac{-184}{-440} \\ \\
{\O}&=&\text{cos}^{-1}\left(\dfrac{-184}{-440}\right) \\ \\
{\O}&=&65.3^{\circ}
\end{array}\) - \(\begin{array}{rrl}
\\ \\ \\ \\ \\
\dfrac{y}{\text{sin }25^{\circ}}&=&\dfrac{20\text{ m}}{\text{sin }28^{\circ}} \\ \\
y&=&\dfrac{20\text{ m sin }25^{\circ}}{\text{sin }28^{\circ}} \\ \\
y&=&18\text{ m}
\end{array}\)
