Law of Sines

Question ▪ How would you solve for the missing side of this triangle? ▪ How would you solve for the missing side given this triangle? 6 X 8 6 X 8

When the triangle isn’t a right triangle ▪ Let’s see how to apply trigonometry to working with triangles that do not contain a right triangle. a c b A C B The ratios of each side to the sine of its “partner” are equal to each other. If the problem refers to 2 sides and 2 angles, USE LAW OF SINES!

How the Law of Sines Work ▪ These ratios, in pairs, are applied to solving triangle problems where: – The triangle is NOT a right triangle – When you have 2 sides and the appropriate angle. ▪ You never need to use all three ratios at the same time. You can mix and match the ratios to correspond with the letters you need. ▪ Remember when working with proportions, cross multiple to solve.

▪ There are 3 cases for which we can use the law of sines. – Angle, Angle, Side (AAS) – Angle, Side, Angle (ASA) – Side, Side, Angle (This case will be discussed in great detail tomorrow)

Example 1: AAS Case (2 angles and a non- adjacent side) ▪ Given C=102.3 degrees, B=28.7 degrees and b=27.4 feet, solve the triangle (find the remaining angles and sides). Round all answers to the nearest tenth.

You Try 1:

Example 2: ASA Case (2 angles and the included side) ▪ Given c=22 feet, B=98 degrees and A=43 degrees, solve the triangle (find remaining angles and sides). Round answers to the nearest tenth.

You Try 2:

Example 3: Solve the triangle. Round answers to the nearest tenth

You Try 3: Solve the triangle. Round answers to the nearest tenth

▪ These are the BASIC cases for the Law of Sines. Tomorrow we will examine “Ambiguous Case” in which numerous possibilities exist. ▪ If you do not get the basics down from today, you WILL have a difficult time with the third case we will do tomorrow.

Homework Worksheet: Assignment 1