Academy Algebra II/Trig

13.5, 13.6 (PC 6.1, 6.2): Law of Sines & CosinesHW: p. 894 (2-8 even)HW Monday: p.894 (9-12 all)Quiz 13.5, 13.6: Tues, 5/12

Solving triangles (other than right triangles) Law of Sines

Law of Cosines

C

c

B

b

A

a

sinsinsin

Cabbac

Baccab

Abccba

cos2

cos2

cos2

222

222

222

The formula you choose depends on the information you are given.

B

A C

a

b

c

1.) Solve the triangle with the following:

B

A C

a

b

c

8,48,36 aBA

2.) Solve the triangle with the following:

B

A C

a

b

c

42,7,4 Aba

3.) Solve the triangle with the following:

B

A C

a

b

c

30,6,7 Bba

Do Now: Solve the triangle with the following.

B

A C

a

b

c

42,12,22 Aba

Solve the triangle with the following:B

A C

a

b

c

5,7,9 cba

Solve the triangle with the following:B

A C

a

b

c

115,10,15 Acb

Area of a Triangle

B

A C

a

b

c

BacCabAbc sin2

1sin

2

1sin

2

1 Area

2 where

Area

cbas

csbsass

Heron’s Formula

Do NowIn major league baseball, the four bases form a square whose sides are 90 feet. The front edge of the pitching rubber on which the pitcher stands, is 60.5 feet from home plate.a.) Find the distance from the front edge of the pitching rubber to 1st base.b.) Find the measure of the angle formed by 1st base, the pitching rubber and home plate.

Find the area of the triangle:B

A C

a

b

c

110,10,6 Cba

Find the area of the triangle:B

A C

a

b

c

4,3,2 cba

Find the area of the triangle:B

A C

a

b

c

5438,85,67 Acb

Find the area of the triangle:B

A C

a

b

c

10,9,5 cba

ExampleForest Ranger Rich is at an observation point A along a straight road. He observes a fire in the direction 32o east of north. Forest Ranger Sara is at a second observation point B 10 miles due east of Rich. Sara sights the same fire 48o west of north. Find the distance from each ranger to the fire and find the shortest distance from the fire to the road.

ExampleThe course for a boat race starts at a point and proceeds in the direction S52oW to a point B, and in the direction S40oE to point C, and finally back to point A. The point C lies 8 km directly south of point A. What is the length of the total course?

HW Monday: p.894 (9-12 all)Quiz 13.5, 13.6: Tues, 5/12