Answer Key 11.8
- [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrl} 20^2&=&28^2+28^2-2(28)(28)\text{ cos }{\theta} \\ \\ 400&=&784+784-1568\text{ cos }{\theta} \\ \\ \text{cos }{\theta}&=&\dfrac{-1168}{-1568} \\ \\ {\theta}&=&\text{cos}^{-1}0.7449 \\ \\ {\theta}&=&41.8^{\circ} \end{array}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrl} 140^2&=&200^2+130^2-2(200)(130)\text{ cos }{\theta} \\ \\ 19600&=&400000+169000-52000\text{ cos }{\theta} \\ \\ \text{cos }{\theta}&=&\dfrac{-37300}{-52000} \\ \\ {\theta}&=&\text{cos}^{-1}0.71730 \\ \\ {\theta}&=&44.2^{\circ} \end{array}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrl} 18^2&=&3^2+20^2-2(3)(20)\text{ cos }{\theta} \\ \\ 324&=&9+400-120\text{ cos }{\theta} \\ \\ \text{cos }{\theta}&=&\dfrac{-85}{-120} \\ \\ {\theta}&=&\text{cos}^{-1}\left(\dfrac{-85}{-120}\right) \\ \\ {\theta}&=&44.9^{\circ} \end{array}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrl} 20^2&=&15^2+30^2-2(15)(30)\text{ cos }{\theta} \\ \\ 400&=&225+900-900\text{ cos }{\theta} \\ \\ \text{ cos }{\theta}&=&\dfrac{-725}{-900} \\ \\ {\theta}&=&\text{cos}^{-1}\left(\dfrac{-725}{-900}\right) \\ \\ {\theta}&=&36.3^{\circ} \end{array}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrl} 16^2&=&10^2+8^2-2(8)(10)\text{ cos}{\theta} \\ \\ 256&=&100+64-160\text{ cos }{\theta} \\ \\ \text{ cos }{\theta}&=&\dfrac{92}{-160} \\ \\ {\theta}&=&\text{ cos }^{-1}-0.575 \\ \\ {\theta}&=&125^{\circ} \end{array}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{rrl} 20^2&=&10^2+22^2-2(10)(22)\text{ cos }{\theta} \\ \\ 400&=&100+484-440\text{ cos }{\theta} \\ \\ \text{ cos }{\theta}&=&\dfrac{-184}{-440} \\ \\ {\theta}&=&\text{cos}^{-1}\left(\dfrac{-184}{-440}\right) \\ \\ {\theta}&=&65.3^{\circ} \end{array}[/latex] - [latex]\phantom{a}[/latex]
[latex]\begin{array}[t]{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}[/latex]
