A boat runs in a straight line for 3 kilometers,then makes a turn and goes for another6

In Exercises 116, solve the triangle ABC under the given conditions. A 20, b 10, c 7

In Exercises 116, solve the triangle ABC under the given conditions. B 40, a 12, c 20

In Exercises 116, solve the triangle ABC under the given conditions. C 118, a 6, b 10

In Exercises 116, solve the triangle ABC under the given conditions. C 52.5, a 6.5, b 9

In Exercises 116, solve the triangle ABC under the given conditions. A 140, b 12, c 14

In Exercises 116, solve the triangle ABC under the given conditions. B 25.4, a 6.8, c 10.5

In Exercises 116, solve the triangle ABC under the given conditions. C 78.6, a 12.1, b 20.3

In Exercises 116, solve the triangle ABC under the given conditions. A 118.2, b 16.5, c 10.7

In Exercises 116, solve the triangle ABC under the given conditions. a 7, b 3, c 5

In Exercises 116, solve the triangle ABC under the given conditions. a 8, b 5, c 10

In Exercises 116, solve the triangle ABC under the given conditions. a 16, b 20, c 32

In Exercises 116, solve the triangle ABC under the given conditions. a 5.3, b 7.2, c 10

In Exercises 116, solve the triangle ABC under the given conditions. a 7.2, b 6.5, c 11

In Exercises 116, solve the triangle ABC under the given conditions. a 6.8, b 12.4, c 15.1

In Exercises 116, solve the triangle ABC under the given conditions. a 12, b 16.5, c 21.3

In Exercises 116, solve the triangle ABC under the given conditions. a 5.7, b 20.4, c 16.8

Find the angles of the triangle whose vertices are 10, 02, 15, 22, 11, 42.

Find the angles of the triangle whose vertices are 13, 42, 16, 12, and 12, 12.

Two trains leave a station on different tracks. The tracks make a angle with the station as 112angle with the station as vertex. The first train travels at an average speed of 90 kilometers per hour and the second at an average speed of 55 kilometers per hour. How far apart are the trains after 2 hours and 45 minutes?

One plane flies west from Cleveland at 350 miles per hour. A second plane leaves Cleveland at the same time and flies southeast at 200 miles per hour. How far apart are the planes after 1 hour and 36 minutes?

The pitchers mound on a standard baseball diamond (which is actually a square) is 60.5 feet from home plate. How far is the pitchers mound from first base?

If the straight-line distance from home plate over second base to the center field wall in a baseball stadium is 400 feet, how far is it from first base to the same point in center field? Adapt the figure above.

A stake is located 10.8 feet from the end of a closed gate that is 8 feet long. The gate swings open, and its end hits the stake. Through what angle does the gate swing?

The distance from Chicago to St. Louis is 440 kilometers, from St. Louis to Atlanta 795 kilometers, and from Atlanta to Chicago 950 kilometers. What are the angles in the triangle with these three cities as vertices?

A boat runs in a straight line for 3 kilometers, then makes a turn and goes for another 6 kilometers. How far is the boat from its starting point?

A plane flies in a straight line at 400 miles per hour for 1 hour and 12 minutes. It makes a turn and flies at 375 miles per hour for 2 hours and 27 minutes. How far is it from its starting point?

The side of a hill makes an angle of with the horizontal. A wire is to be run from the top of a 175-foot tower on the top of the hill to a stake located 120 feet down the hillside from the base of the tower. What length of wire is needed?

Two ships leave port, one traveling in a straight course at 22 miles per hour and the other traveling a straight course at 31 miles per hour. Their courses diverge by How far apart are they after 3 hours?

An engineer wants to measure the width CD of a sinkhole. He places a stake B and determines the measurements shown in the figure below. How wide is the sinkhole?

A straight tunnel is to be dug through a hill. Two people stand on opposite sides of the hill where the tunnel entrances are to be located. Both can see a stake located 530 meters from the first person and 755 meters from the second. The angle determined by the two people and the stake (the vertex) is How long must the tunnel be?

One diagonal of a parallelogram is 6 centimeters long, and the other is 13 centimeters long. They form an angle of with each other. How long are the sides of the parallelogram?

A parallelogram has diagonals of lengths 12 and 15 inches that intersect at an angle of How long are the sides of the parallelogram?

A ship is traveling at 18 miles per hour from Corsica to Barcelona, a distance of 350 miles. To avoid bad weather, the ship leaves Corsica on a route south of the direct route (see the figure below). After 7 hours the bad weather has been bypassed. Through what angle should the ship now turn to head directly to Barcelona?

In aerial navigation, directions are given in degrees clockwise from north. Thus east is south is and so on, as shown in the following figure. A plane leaves South Bend for Buffalo, 400 miles away, intending to fly a straight course in the direction After flying 180 miles, the pilot realizes that an error has been made and that he has actually been flying in the direction 55 a. At that time, how far is the plane from Buffalo? b. In what direction should the plane now go to reach Buffalo?

Assume that the earth is a sphere of radius 3980 miles. A satellite travels in a circular orbit around the earth, 900 miles above the equator, making one full orbit every 6 hours. If it passes directly over a tracking station at 2 P.M., what is the distance from the satellite to the tracking station at 2:05 P.M.?

Two planes at the same altitude approach an airport. One plane is 16 miles from the control tower and the other is 22 miles from the tower. The angle determined by the planes and the tower, with the tower as the vertex, is How far apart are the planes?

Assuming that the circles in the following figure are mutually tangent, find the lengths of the sides and the measures of the angles in triangle ABC.

Assuming that the circles in the following figure are mutually tangent, find the lengths of the sides and the measures of the angles in triangle ABC.

Critical Thinking A rope is attached at points A and B and taut around a pulley whose center is at C, as shown in the following figure. The rope lies on the pulley from D to E and the radius of the pulley is 1 meter. How long is the rope?

Critical Thinking Use the Law of Cosines to prove that the sum of the squares of the lengths of the two diagonals of a parallelogram equals the sum of the squares of the lengths of the four sides.