Pre-Calc: 6.1-6.2

Law of SinesLaw of Cosines

BINGO!

Use Law of Sines to solve the triangle:

• Use Law of Sines to solve the triangle

A = 102.4° C = 16.7° a = 21.6

• Because of prevailing winds, a tree grew so that it was leaning 4° from the vertical. At a point 40 meters from the tree, the angle of elevation to the top of the tree is 30°. Find the height h, of the tree.

• Use Law of Cosines to solve the triangle.

C b= 12 a = 10

A B c = 16

Use Law of Cosines to solve the triangle:

A = 120° b = 6 c = 7

• To approximate the length of a marsh, a surveyor walks 250 meters from point A to point B, then turns and walks 220 meters to point C. Approximate the length AC of the marsh.

• Use Heron’s Formula to find the area of the triangle with the following sides:

a = 8 b = 12 c = 17

• Use Law of Sines to solve the triangle:

• Use Law of Sines to solve the triangle:

A = 120° B = 45° c = 16

• Find the area of the triangle:

A = 150° b = 8 c = 10

• Because of prevailing winds, a tree grew so that it was leaning 3° from the vertical. At a point 20 meters from the tree, the angle of elevation to the top of the tree is 28°. Find the height h of the tree.

• Use Law of Cosines to solve the triangle:

C b=15 a

A = 30° B c = 30

• Use Law of Cosines to solve the triangle:

a = 55 b = 25 c = 72

Determine whether Law of Sines or Cosines is used to solve the triangle.

a = 10 b = 12 c = 70

• 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 420 feet from the camera. The camera turns 8°to follow the play. Approximately how far does the center fielder have to run to make the catch?

• Use Heron’s Formula to find the area of the triangle.

a = 3.05 b = .75 c = 2.45

• Determine whether to use Law of Sines or Cosines to solve the triangle:

A = 42° B = 35° c = 1.2

• Determine the angle Θ in the design of the streetlight shown in the figure.

Use Law of Sines to solve the triangle:

• Use Law of Sines to solve the triangle:

A = 55° B = 42° c = ¾

• Find the Area of the trianle:

C = 170° a = 14 b = 24

• The angles of elevation to an airplane from two points A and B on level ground are 55° and 72°, respectively. The points A and B are 2.2 miles apart, and the airplane is east of both points in the same vertical plane. Find the altitude of the plane.

Use Law of Cosines to solve the triangle.

• Use Law of Cosines to solve the triangle:

A = 48° b = 3 c = 14