Acute and Obtuse Triangles
Pacing:This lesson could take two to four class periods
Goal:The purpose of this lesson is to extend trigonometric ratios to non-right triangles. This is done using to new
laws: the Law of Sines and the Law of Cosines. The Law of Sines is much easier to present to students than the
Law of Cosines. The Law of Sines uses proportions, while the Law of Cosines uses a general form of Pythagorean’s
Theorem.
Shortcut!Students confuse themselves regarding which law to use. A shortcut to use is as follows: If the triangle has
more side information than angle information, use the Law of Cosines. If the triangle has more angle information
than side information, use the Law of Sines. And of course, if you cannot solve it with the law you have chosen,
“Choose the Other One!”
Relate to Triangle Similarity!Have students recall the five basic types of triangle similarity: SSS, SAS, AAS, AAA,
ASA. Reading the given information from left to right, if the information ends in an “angle,” use the Law of Sines.
If the information ends in a “side,” use the Law of Cosines.
Additional Examples:
- A fire is spotted in Yellowstone National Park by two forest ranger stations. Fire Station A is 15 km from Fire
Station B. The angle at which the fire is spotted by Fire Station B is 75 and the angle at which the fire is spotted by
Fire Station A is 70 degrees.Which fire station should report to the fire?AB= 25 .26 kmand BC= 24. 57 .Therefore,
Fire Station A should report to the fire. - Suppose 4 ABChas the following values:m^6 C= 40 ,a= 8 ,b= 9 .Findc.c= 5. 89
Chapter 1. Geometry TE - Teaching Tips