Academy Algebra II/Trig 13.5, 13.6 (PC 6.1, 6.2): Law of Sines & Cosines HW: p. 894 (2-8 even) HW Monday: p.894 (9-12 all) Quiz 13.5, 13.6: Tues, 5/12
Jan 03, 2016
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