Law of SinesAdvanced Algebra with Applications

Mrs. Kathy GordonConcordia International School Shanghai

An AAS Case Solve ΔABC with C = 103˚, B = 28˚ and b =

26 feet. Before you work through this powerpoint, you

should have already watched the 5.5a Law of Sines video on Zaption.com. If you have not watched it yet, START THERE, then come back to this powerpoint.

Based on the information shared in 5.5a Law of Sines, solve this triangle. When you think you have worked it out, proceed through the Powerpoint to check your work.

An AAS Case Solve ΔABC with C = 103˚, B = 28˚ and b =

26 feet. Suggestion 1: If you are not given a

diagram, make a quick sketch of one and label what you are given.

An AAS Case Solve ΔABC with C = 103˚, B = 28˚ and b =

26 feet. Suggestion 2: Make a quick table of the six

parts of a triangle and fill in what you know. This will help you keep your information organized.A = a =

B = 28˚ b = 26 ft.

C = 103˚ c =

An AAS Case Solve ΔABC with C = 103˚, B = 28˚ and b =

26 feet. We can find angle A from the fact that the

angles of a triangle have to add up to 180˚.

180 – 28 – 103 = 49A = a =

B = 28˚ b = 26 ft.

C = 103˚ c =

An AAS Case Solve ΔABC with C = 103˚, B = 28˚ and b =

26 feet. We can find angle A from the fact that the

angles of a triangle have to add up to 180˚.

180 – 28 – 103 = 49A = 49˚ a =

B = 28˚ b = 26 ft.

C = 103˚ c =

An AAS Case Solve ΔABC with C = 103˚, B = 28˚ and b =

26 feet. Now use the Law of Sines to set up ratios and

find the missing sides.

A = 49˚ a =

B = 28˚ b = 26 ft.

C = 103˚ c =

Side a:

Use your calculator to solve.Make sure it is in degree mode.

An AAS Case Solve ΔABC with C = 103˚, B = 28˚ and b =

26 feet. Now use the Law of Sines to set up ratios and

find the missing sides.

A = 49˚ a ≈ 41.8 ft.

B = 28˚ b = 26 ft.

C = 103˚ c =

Side c:

Use your calculator to solve.Make sure it is in degree mode.

An AAS Case Solve ΔABC with C = 103˚, B = 28˚ and b =

26 feet. Now use the Law of Sines to set up ratios and

find the missing sides.

A = 49˚ a ≈ 41.8 ft.

B = 28˚ b = 26 ft.

C = 103˚ c ≈ 54.0 ft.

Your triangle is solved!

Can this help us find area? Continue to find out --- >

Area of a Triangle Normally, we find area of a triangle using:

But what happens when we don’t know the height, and it is not easy to figure out? We have another option:

Area of a Triangle. Find the area of ΔABC.

Since we are given angle A, we use the version with angle A.

Substitute:

Use your calculator:

5.5 Practice – NEW Directions

#1 – 7: Solve the triangle with the measurements given. IF THE TRIANGLE IS NOT POSSIBLE, then say so for your answer. Ignore the part about two triangles.

Use this diagram for problem #12: