Chapter 7

Use the Law of sines to solve the triangle. \(A=110^{\circ}, \quad a=125, \quad b=100\)

Use the dot product to find the magnitude of \(\mathbf{u}.\) $$\mathbf{u}=\langle-8,15\rangle$$

Use the Law of cosines to solve the triangle. $$A=48^{\circ}, \quad b=3, \quad c=14$$

Use the dot product to find the magnitude of \(\mathbf{u}.\) $$\mathbf{u}=20 \mathbf{i}+25 \mathbf{j}$$

Use the Law of cosines to solve the triangle. $$a=75.4, \quad b=48, \quad c=48$$

Use the dot product to find the magnitude of \(\mathbf{u}.\) $$\mathbf{u}=6 \mathbf{i}-10 \mathbf{j}$$

Use the Law of cosines to solve the triangle. $$a=1.42, \quad b=0.75, \quad c=1.25$$

Use the dot product to find the magnitude of \(\mathbf{u}.\) $$\mathbf{u}=-4 \mathbf{j}$$

Use the Law of cosines to solve the triangle. $$B=8^{\circ} 15^{\prime}, \quad a=26, \quad c=18$$

Use the Law of sines to solve the triangle. \(B=28^{\circ}, \quad C=104^{\circ}, \quad a=3 \frac{5}{8}\)

Use the dot product to find the magnitude of \(\mathbf{u}.\) $$\mathbf{u}=9 \mathbf{i}$$

Use the Law of cosines to solve the triangle. $$B=10^{\circ} 35^{\prime}, \quad a=40, \quad c=30$$

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=\langle-1,0\rangle\\\ &\mathbf{v}=\langle 0,2\rangle \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$-8 i$$

Use the Law of cosines to solve the triangle. $$C=43^{\circ}, \quad a=\frac{4}{9}, \quad b=\frac{7}{9}$$

Use the Law of sines to solve the triangle. \(A=110^{\circ} 15^{\prime}, \quad a=48, \quad b=16\)

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=\langle 4,4\rangle\\\ &\mathbf{v}=\langle-2,0\rangle \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$4 i$$

Use the Law of cosines to solve the triangle. $$C=101^{\circ}, \quad a=\frac{3}{8}, \quad b=\frac{3}{4}$$

Use the Law of sines to solve the triangle. \(B=2^{\circ} 45^{\prime}, \quad b=6.2, \quad c=5.8\)

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=2 \mathbf{i}+6 \mathbf{j}\\\ &\mathbf{v}=-5 \mathbf{i}+2 \mathbf{j} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$5 i$$

Use the Law of Sines to solve the triangle. If two solutions exist, find both. \(A=76^{\circ}, \quad a=18, \quad b=20\)

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=7 \mathbf{i}-2 \mathbf{j}\\\ &\mathbf{v}=-8 \mathbf{i}+6 \mathbf{j} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$-10 i$$

Use the Law of Sines to solve the triangle. If two solutions exist, find both. \(A=110^{\circ}, \quad a=125, \quad b=200\)

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=2 \mathbf{i}\\\ &\mathbf{v}=-3 \mathbf{j} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$7-7 i$$

Use the Law of Sines to solve the triangle. If two solutions exist, find both. \(A=120^{\circ}, \quad a=b=25\)

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=4 \mathbf{j}\\\ &\mathbf{v}=-9 \mathbf{i} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$2+2 i$$

Use the Law of Sines to solve the triangle. If two solutions exist, find both. \(A=60^{\circ}, \quad a=9, \quad c=10\)

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=\cos \left(\frac{\pi}{3}\right) \mathbf{i}+\sin \left(\frac{\pi}{3}\right) \mathbf{j}\\\ &\mathbf{v}=\cos \left(\frac{3 \pi}{4}\right) \mathbf{i}+\sin \left(\frac{3 \pi}{4}\right) \mathbf{j} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$\sqrt{3}+i$$

Use the Law of Sines to solve the triangle. If two solutions exist, find both. \(A=58^{\circ}, \quad a=11.4, \quad b=12.8\)

Find the angle \(\theta\) between the vectors. $$\begin{aligned} &\mathbf{u}=\cos \left(\frac{\pi}{4}\right) \mathbf{i}+\sin \left(\frac{\pi}{4}\right) \mathbf{j}\\\ &\mathbf{v}=\cos \left(\frac{2 \pi}{3}\right) \mathbf{i}+\sin \left(\frac{2 \pi}{3}\right) \mathbf{j} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$1-\sqrt{3} i$$

Use the Law of Sines to solve the triangle. If two solutions exist, find both. \(A=58^{\circ}, \quad a=4.5, \quad b=12.8\)

Graph the vectors and find the degree measure of the angle between the vectors. $$\begin{aligned} &\mathbf{u}=2 \mathbf{i}-4 \mathbf{j}\\\ &\mathbf{v}=3 \mathbf{i}-5 \mathbf{j} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$1+i$$

Graph the vectors and find the degree measure of the angle between the vectors. $$\begin{aligned} &\mathbf{u}=6 \mathbf{i}-2 \mathbf{j}\\\ &\mathbf{v}=8 \mathbf{i}-5 \mathbf{j} \end{aligned}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$4-4 i$$

Graph the vectors and find the degree measure of the angle between the vectors. $$\begin{aligned} &\mathbf{u}=6 \mathbf{i}-2 \mathbf{j}\\\ &\mathbf{v}=8 \mathbf{i}-5 \mathbf{j} \end{aligned}$$

Determine whether the Law of sines or the Law of cosines can be used to find another measure of the triangle. Then solve the triangle. $$a=8, \quad c=5, \quad B=40^{\circ}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$-2(1+\sqrt{3} i)$$

Graph the vectors and find the degree measure of the angle between the vectors. $$\begin{aligned} &\mathbf{u}=-7 \mathbf{i}-4 \mathbf{j}\\\ &\mathbf{v}=-8 \mathbf{i}+2 \mathbf{j} \end{aligned}$$

Determine whether the Law of sines or the Law of cosines can be used to find another measure of the triangle. Then solve the triangle. $$a=10, \quad b=12, \quad C=70^{\circ}$$

Represent the complex number graphically, and find the trigonometric form of the number. $$-\frac{5}{2}(\sqrt{3}+i)$$

Use vectors to find the interior angles of the triangle with the given vertices. $$(1,2), (3,4), (2,5)$$

Determine whether the Law of sines or the Law of cosines can be used to find another measure of the triangle. Then solve the triangle. $$A=24^{\circ}, \quad a=4, \quad b=18$$