Solving a Triangle In Exercises 3136, determine whether the Law of Sines or the Law of

Fill in the blanks. When you are given three sides of a triangle, you use the Law of ________ to find the three angles of the triangle.

Fill in the blanks. When you are given two angles and any side of a triangle, you use the Law of ________ to solve the triangle.

Fill in the blanks. The standard form of the Law of Cosines for is ________ .

Fill in the blanks. The Law of Cosines can be used to establish a formula for finding the area of a triangle called ________ ________ Formula.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Using the Law of Cosines In Exercises 524, use the Law of Cosines to solve the triangle. Round your answers to two decimal places.

Finding Measures in a Parallelogram In Exercises 2530, complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by and )

Finding Measures in a Parallelogram In Exercises 2530, complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by and )

Finding Measures in a Parallelogram In Exercises 2530, complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by and )

Finding Measures in a Parallelogram In Exercises 2530, complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by and )

Finding Measures in a Parallelogram In Exercises 2530, complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by and )

Finding Measures in a Parallelogram In Exercises 2530, complete the table by solving the parallelogram shown in the figure. (The lengths of the diagonals are given by and )

Solving a Triangle In Exercises 3136, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places.

Solving a Triangle In Exercises 3136, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places.

Solving a Triangle In Exercises 3136, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places.

Solving a Triangle In Exercises 3136, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places.

Solving a Triangle In Exercises 3136, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places.

Solving a Triangle In Exercises 3136, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places.

Using Herons Area Formula In Exercises 3744, use Herons Area Formula to find the area of the triangle.

Using Herons Area Formula In Exercises 3744, use Herons Area Formula to find the area of the triangle.

Using Herons Area Formula In Exercises 3744, use Herons Area Formula to find the area of the triangle.

Using Herons Area Formula In Exercises 3744, use Herons Area Formula to find the area of the triangle.

Using Herons Area Formula In Exercises 3744, use Herons Area Formula to find the area of the triangle.

Using Herons Area Formula In Exercises 3744, use Herons Area Formula to find the area of the triangle.

Using Herons Area Formula In Exercises 3744, use Herons Area Formula to find the area of the triangle.

Using Herons Area Formula In Exercises 3744, use Herons Area Formula to find the area of the triangle.

Navigation A boat race runs along a triangular course marked by buoys and The race starts with the boats headed west for 3700 meters. The other two sides of the course lie to the north of the first side, and their lengths are 1700 meters and 3000 meters. Draw a figure that gives a visual representation of the situation. Then find the bearings for the last two legs of the race.

Navigation A plane flies 810 miles from Franklin to Centerville with a bearing of Then it flies 648 miles from Centerville to Rosemount with a bearing of Draw a figure that visually represents the situation. Then find the straight-line distance and bearing from Franklin to Rosemount.

Surveying To approximate the length of a marsh, a surveyor walks 250 meters from point to point , then turns and walks 220 meters to point (see figure). Approximate the length of the marsh.

Streetlight Design Determine the angle in the design of the streetlight shown in the figure.

Distance Two ships leave a port at 9 A.M. One travels at a bearing of N W at 12 miles per hour, and the other travels at a bearing of S W at 16 miles per hour. Approximate how far apart they are at noon that day.

Length A 100-foot vertical tower is to be erected on the side of a hill that makes a angle with the horizontal (see figure). Find the length of each of the two guy wires that will be anchored 75 feet uphill and downhill from the base of the tower.

Navigation On a map, Minneapolis is 165 millimeters due west of Albany, Phoenix is 216 millimeters from Minneapolis, and Phoenix is 368 millimeters from Albany (see figure). (a) Find the bearing of Minneapolis from Phoenix. (b) Find the bearing of Albany from Phoenix.

Baseball The baseball player in center field is playing approximately 330 feet from the television camera that is behind home plate. A batter hits a fly ball that goes to the wall 420 feet from the camera (see figure). The camera turns to follow the play. Approximately how far does the center fielder have to run to make the catch?

Baseball On a baseball diamond with 90-foot sides, the pitchers mound is 60.5 feet from home plate. How far is it from the pitchers mound to third base?

Surveying A triangular parcel of land has 115 meters of frontage, and the other boundaries have lengths of 76 meters and 92 meters. What angles does the frontage make with the two other boundaries?

Surveying A triangular parcel of ground has sides of lengths 725 feet, 650 feet, and 575 feet. Find the measure of the largest angle.

Engine Design An engine has a seven-inch connecting rod fastened to a crank (see figure). (a) Use the Law of Cosines to write an equation giving the relationship between and (b) Write as a function of (Select the sign that yields positive values of ) (c) Use a graphing utility to graph the function in part (b). (d) Use the graph in part (c) to determine the total distance the piston moves in one cycle.

Geometry The lengths of the sides of a triangular parcel of land are approximately 200 feet, 500 feet, and 600 feet. Approximate the area of the parcel.

Geometry A parking lot has the shape of a parallelogram (see figure). The lengths of two adjacent sides are 70 meters and 100 meters. The angle between the two sides is What is the area of the parking lot?

Geometry You want to buy a triangular lot measuring 510 yards by 840 yards by 1120 yards. The price of the land is $2000 per acre. How much does the land cost? (Hint:

Geometry You want to buy a triangular lot measuring 1350 feet by 1860 feet by 2490 feet. The price of the land is $2200 per acre. How much does the land cost? (Hint:

In Herons Area Formula, is the average of the lengths of the three sides of the triangle.

In addition to SSS and SAS, the Law of Cosines can be used to solve triangles with AAS conditions.

Think About It What familiar formula do you obtain when you use the standard form of the Law of Cosines and you let What is the relationship between the Law of Cosines and this formula?

Writing Describe how the Law of Cosines can be used to solve the ambiguous case of the oblique triangle where feet, feet, and Is the result the same as when the Law of Sines is used to solve the triangle? Describe the advantages and the disadvantages of each method.

Writing In Exercise 64, the Law of Cosines was used to solve a triangle in the two-solution case of SSA. Can the Law of Cosines be used to solve the no-solution and single-solution cases of SSA? Explain.

HOW DO YOU SEE IT? Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.

Proof Use the Law of Cosines to prove that

Proof Use the Law of Cosines to prove that 1 2 bc_1 _ cos A_ _ a _ b _ c 2 _ a _ b _ c 2 .