page+25


 * **How do we determine the appropriate formulas to use in solving triangle problems?**

After this lesson, you will be able to...
 * 1) explain when trigonometry of the right triangle is used to find lengths or measures of angles
 * 2) explain when the Law of Sines is use to find the lengths of sides or measures of angles.
 * 3) explain when the Law of Cosines is used to find the lengths of sides or measures of angles
 * 4) solve problems involving any combination of the Law of sines, the Law of cosines, and the trigonometry of the right triangle
 * 5) solve numerical examples involving trigonometric ratios, including angle of elevation.

In this lesson there will be no videos. There are just a few notes to take then some questions to answer before you begin your class work.


 * **Notes**
 * The Laws of Sines and Cosines work for non-right triangles
 * Plain old sin, cos and tan (like you learned in 9th grade) will only work on right triangles.


 * **Questions**


 * What information on a triangle do you need to use the Law of Sines?
 * What information on a triangle do you need to use the Law of Cosines?


 * **Classwork:** Solve. Be sure to use the proper method. Draw a picture first to help you.

The Parks Department is laying out a nature trail through the woods that is to consist of three straight paths that form a triangle. The lengths of two paths measure 1.2 miles and 1.5 miles. What must be the measure of the angle between these two sections of the path in order that the total length of the nature trail will be 4.0 miles? (Ans: 56°)


 * **Homework:** do the problems that are multiples of three

[|Solving_for_Triangles,_1.JPG]

[|Solving_for_Triangles,_2.JPG]


 * Answers:

[|A-Area_of_Triangles.JPG]


 * **Journal entry:** Often it is not possible to make measurements directly, as in the case of determining the elevation of a mountain peak. Describe how the Law of Sines and the Law of Cosines can help with measurements.