Chapter 5 Law of Sines and
Cosines
The Story
There are 3 cities in California (knows how to
party):
City A
City B
City C
The cities on the map make up a triangle. If people
want to find and travel the distance between cities,
Or the angles on the map, what should they do?
Use the Law of Sines!
𝑎
𝑏
𝑐
=
=
𝑆𝑖𝑛(𝐴) 𝑆𝑖𝑛(𝐵) 𝑆𝑖𝑛(𝐶)
𝑎𝑖𝑟𝑝𝑙𝑎𝑛𝑒 𝑏𝑜𝑎𝑡
𝑐𝑎𝑟𝑠
=
=
𝐴𝑖𝑟𝑝𝑜𝑟𝑡 𝐵𝑎𝑦 𝐶𝑎𝑟𝑝𝑜𝑟𝑡
Little a is the route
airplanes travel on
A
Little b is the route boats
travel
b
c
Little c is the route cars
travel
A= airport
B=bay
C= carport
B
C
a
Law of Cosines
a²=b²+c²- 2bc(cosA)
Airplane²= boat² + cars²2boatcar(Airport)
Airplanes can travel over sea and land, and are
better than boats and cars. That’s why they go first.
However, the letters are interchangeable,
as long as you keep the same format (ex
c²=a²+b²- 2ab(cosC)