Find the required horizontal and vertical components of the given vectors.
A car is being unloaded from a ship. It is supported by a cable from a crane and guided into position by a horizontal rope. If the tension in the cable is $2790 \mathrm{lb}$ and the cable makes an angle of $3.5^{\circ}$ with the vertical, what are the weight $W$ of the car and the tension $T$ in the rope? (The weight of the cable is negligible to that of the car.)

Find the required horizontal and vertical components of the given vectors.
A wind-blown fire with a speed of $18 \mathrm{ft} / \mathrm{s}$ is moving toward a highway at an angle of $66^{\circ}$ with the highway. What is the component of the velocity toward the highway?

Add the given vectors by using the trigonometric functions and the Pythagorean theorem.
$R=630, \theta_R=189.6^{\circ}$

$$F=176, \theta_F=320.1^{\circ}$$

$$T=324, \theta_T=75.4^{\circ}$$

Solve the given problems.
A block of ice slides down a (frictionless) ramp with an acceleration of $5.3 \mathrm{~m} / \mathrm{s}^2$. If the ramp makes an angle of $32.7^{\circ}$ with the horizontal, find $g$, the acceleration due to gravity.

Solve the triangles with the given parts. \

$$A=71.0^{\circ}, B=48.5^{\circ}, c=8.42$$

Find the indicated vector sums and differences with the given vectors by means of diagrams. (You might find graph paper to be helpful.)
$\mathrm{D}+\mathbf{E}$

Add the given vectors by using the trigonometric functions and the Pythagorean theorem. \

$$A=21.9, \theta_A=236.2^{\circ}$$

$$B=96.7, \theta_B=11.5^{\circ}$$

$$C=62.9, \theta_C=143.4^{\circ}$$

Solve the triangles with the given parts.
$a=20, c=10, C=30^{\circ}$

Solve the triangles with the given parts. \

$$A=17.85^{\circ}, B=154.16^{\circ}, c=7863$$

Find the required horizontal and vertical components of the given vectors.
A nuclear submarine approaches the surface of the ocean at $25.0 \mathrm{~km} / \mathrm{h}$ and at an angle of $17.3^{\circ}$ with the surface. What are the components of its velocity?

Solve the triangles with the given parts.
$a=17, b=24, c=42$. Explain your answer.

Use the law of cosines to solve the given problems.
An iRobot Roomba vacuum cleaner travels $12.5$ ft across the floor where it then hits a wall and turns on a $47.0^{\circ}$ corner. If it travels $15.0$ ft in this new direction, how far is it from its starting point?

Add the given vectors by using the trigonometric functions and the Pythagorean theorem.
$E=1653, \theta_E=36.37^{\circ}$

$$F=9807, \theta_F=253.06^{\circ}$$

Solve the given problems.
A space shuttle is moving in orbit at $18,250 \mathrm{mi} / \mathrm{h}$. A satellite is launched to the rear at $120 \mathrm{mi} / \mathrm{h}$ at an angle of $5.20^{\circ}$ from the direction of the shuttle. Find the velocity of the satellite.