In this given problem using the Law of Cosines to solve the triangle.

$$\beta=100^{\circ}, a=22.3, b=16.1$$

The length of a Boeing 747 airplane is $231 \mathrm{ft}$. What is the plane's altitude if it subtends an angle of $2^{\circ}$ when it is directly above an observer on the ground? See the earlier figure.

In this given problem using the Law of Cosines to solve the triangle.

$$\alpha=22^{\circ}, b=3, c=9$$

In this given problem using the Law of Sines to solve the triangle.

$$\gamma=150^{\circ}, b=7, c=5$$

In this problem, find $\mathbf{u}-4 \mathbf{v}$ and $2 \mathbf{u}+5 \mathbf{v}$.

$$\mathbf{u}=\mathbf{i}-2 \mathbf{j}, \mathbf{v}=8 \mathbf{i}+3 \mathbf{j}$$

Find the indicated unknowns. For this problem refers to the triangle shown in the earlier figure.

$$b=1.5, c=3 ; \alpha, \beta, a$$

From two lifeguard towers A and B, a swimmer in distress is sighted on bearings of $\mathrm{N} 46^{\circ} \mathrm{E}$ and $\mathrm{N} 27^{\circ} \mathrm{W}$, respectively. If tower B is $250 \mathrm{ft}$ due east of tower A, what is the distance from each tower to the swimmer?

Find the indicated unknowns. For this problem refers to the triangle shown in the earlier figure.

$$c=25, \alpha=50^{\circ} ; a, b$$

In this given problem using the Law of Cosines to solve the triangle.

$$\beta=130^{\circ}, a=4, c=7$$

The angle between two sides of a parallelogram is $40^{\circ}$. If the lengths of the sides are 5 and $10 \mathrm{~cm}$, find the lengths of the two diagonals.

In this given problem using the Law of Sines to solve the triangle.

$$\alpha=55^{\circ}, a=20, c=18$$

In this problem, find $\mathbf{u}+\mathbf{v}, \mathbf{u}-\mathbf{v},-3 \mathbf{u}$, and $3 \mathbf{u}-4 \mathbf{v}$.

$$\mathbf{u}=\langle 0.1,0.2\rangle, \mathbf{v}=\langle-0.3,0.4\rangle$$

In this given problem using the Law of Sines to solve the triangle.

$$\gamma=15^{\circ}, a=8, c=5$$

Find the indicated unknowns. For this problem refers to the triangle shown in the earlier figure.

$$b=8, \beta=34.33^{\circ} ; a, c$$