Chapter 7

Find the exact values of the remaining parts of triangle \(A B C\). $$\alpha=60^{\circ}, \quad b=6, \quad c=7$$

Find the absolute value. $$|3-4 i|$$

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. $$\langle- 2,5\rangle, \quad\langle 3,6\rangle$$

Find \(a+b, a-b, 4 a+5 b, 4 a-5 b,\) and \(\|a\|\) $$\mathbf{a}=\langle 2,-3\rangle, \quad \mathbf{b}=\langle 1,4\rangle$$

Solve \(\triangle A B C\). $$\alpha=41^{\circ}, \quad \gamma=77^{\circ}, \quad a=10.5$$

Find the exact values of the remaining parts of triangle \(A B C\). $$y=30^{\circ}, \quad a=2 \sqrt{3}, \quad c=2$$

Find the absolute value. $$|5+8 i|$$

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. $$(4,-7), \quad(-2,3)$$

Find \(a+b, a-b, 4 a+5 b, 4 a-5 b,\) and \(\|a\|\) $$\mathbf{a}=(-2,6), \quad \mathbf{b}=(2,3)$$

Solve \(\triangle A B C\). $$\beta=20^{\circ}, \quad \gamma=31^{\circ}, \quad b=210$$

Find the exact values of the remaining parts of triangle \(A B C\). $$\alpha=60^{\circ}, \quad \beta=45^{\circ}, \quad b=100$$

Find the absolute value. $$|-6-7 i|$$

Find \(a+b, a-b, 4 a+5 b, 4 a-5 b,\) and \(\|a\|\) $$\mathbf{a}=-(7,-2), \quad \mathbf{b}=4(-2,1)$$

Solve \(\triangle A B C\). $$\alpha=27^{\circ} 40^{\prime}, \quad \beta=52^{\circ} 10^{\prime}, \quad a=32.4$$

Find the absolute value. $$|1-i|$$

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. $$8 \mathbf{i}-3 \mathbf{j}, \quad 2 \mathbf{i}-7 \mathbf{j}$$

Find \(a+b, a-b, 4 a+5 b, 4 a-5 b,\) and \(\|a\|\) $$\mathbf{a}=2\langle 5,-4\rangle, \quad \mathbf{b}=-\langle 6,0\rangle$$

Solve \(\triangle A B C\). $$\beta=50^{\circ} 50^{\prime}, \quad \gamma=70^{\circ} 30^{\prime}, \quad c=537$$

Solve triangle A B C. $$\begin{array}{llll} \quad \alpha=60^{\circ}, & b=20, & c=30\end{array}$$

Approximate the remaining parts of triangle \(A B C\). $$\beta=67^{\circ}, \quad \gamma=75^{\circ}, \quad b=12$$

Find the absolute value. $$|8 i|$$

Find \(a+b, a-b, 4 a+5 b, 4 a-5 b,\) and \(\|a\|\) $$\mathbf{a}=\mathbf{i}+2 \mathbf{j}, \quad \mathbf{b}=3 \mathbf{i}-5 \mathbf{j}$$

Solve \(\triangle A B C\). $$\alpha=42^{\circ} 10^{\prime}, \quad \gamma=61^{\circ} 20^{\prime}, \quad b=19.7$$

Solve triangle A B C. $$\gamma=45^{\circ}, \quad b=10.0, \quad a=15.0$$

Approximate the remaining parts of triangle \(A B C\). $$\alpha=23^{\circ} 30^{\prime}, \quad c=125, \quad a=152$$

Find the absolute value. $$\left|i^{7}\right|$$

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. \(6J\), -\(4I\)

Find \(a+b, a-b, 4 a+5 b, 4 a-5 b,\) and \(\|a\|\) $$\mathbf{a}=-3 \mathbf{i}+\mathbf{j}, \quad \mathbf{b}=-3 \mathbf{i}+\mathbf{j}$$

Solve \(\triangle A B C\). $$\alpha=103.45^{\circ}, \quad \gamma=27.19^{\circ}, \quad b=38.84$$

Solve triangle A B C. $$\beta=150^{\circ}, \quad a=150, \quad c=30$$

Approximate the remaining parts of triangle \(A B C\). $$\beta=115^{\circ}, \quad a=4.6, \quad c=7.3$$

Find the absolute value. $$\left|i^{500}\right|$$

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. $$\langle 10,7\rangle, \quad\left\langle- 2,-\frac{7}{5}\right\rangle$$

Sketch vectors corresponding to \(a, b, a+b\) \(2 a,\) and \(-3 b\) $$\mathbf{a}=3 \mathbf{l}+2 \mathbf{j}, \quad \mathbf{b}=-\mathbf{l}+5 \mathbf{j}$$

Solve \(\triangle A B C\). $$\gamma=81^{\circ}, \quad c=11, \quad b=12$$

Solve triangle A B C. $$\beta=73^{\circ} 50^{\prime}, \quad c=14.0, \quad a=87.0$$

Approximate the remaining parts of triangle \(A B C\). $$a=37, \quad b=55, \quad c=43$$

Find the absolute value. $$|-15 i|$$

Find (a) the dot product of the two vectors and (b) the angle between the two vectors. $$\langle- 3,6\rangle, \quad\langle- 1,2\rangle$$

Sketch vectors corresponding to \(a, b, a+b\) \(2 a,\) and \(-3 b\) $$\mathbf{a}=-5 \mathbf{t}+2 \mathbf{j}, \quad \mathbf{b}=\mathbf{i}-3 \mathbf{j}$$

Solve \(\triangle A B C\). $$\alpha=32.32^{\circ}, \quad c=574.3, \quad a=263.6$$

Solve triangle A B C. $$\gamma=115^{\circ} 10^{\prime}, \quad a=1.10, \quad b=2.10$$

Approximate the area of triangle \(A B C\) to the nearest 0.1 square unit. $$\alpha=75^{\circ}, \quad b=20, \quad c=30$$

Find the absolute value. $$|0|$$

Show that the vectors are orthogonal. $$<4,-1>, \quad<2,8>$$

Sketch vectors corresponding to \(a, b, a+b\) \(2 a,\) and \(-3 b\) $$\mathbf{a}=\langle- 4,6\rangle, \quad \mathbf{b}=\langle- 2,3\rangle$$

Solve \(\triangle A B C\). $$\gamma=53^{\circ} 20^{\prime}, \quad a=140, \quad c=115$$

Approximate the area of triangle \(A B C\) to the nearest 0.1 square unit. $$a=4, \quad b=7, \quad c=10$$

Find the absolute value. $$|-15|$$

Show that the vectors are orthogonal. $$\langle 3,6\rangle, \quad\langle 4,-2\rangle$$