Bellwork

Lesson QuizLesson PresentationLesson 9.5Apply the Law of SinesWarm-UpStandard Accessed: Students will prove, apply, and model trigonometric functions and ratios.1Warm-Up Solve XYZ.

2Essential Understandings

When can the Law of sines be used to solve a triangle?When two angles and the length of any side are known (AAS or ASA cases), or when the lengths of two sides and an angle opposite one of the two sides are known, (SSA). The law of sines is used to solve triangles with no right angle.5VocabularyLaw of Sines:Can be used to solve triangles with no right angle, when two angles and the length of any side are known (AAS or ASA cases), or when the lengths of two sides and an angle opposite one of the two sides are known, (SSA).

4Solve a triangle for the AAS or ASA caseEXAMPLE1SOLUTION3. Write the Law of Sine proportion1. Draw a picture 4. Write the Law of Sine proportion6Solve a triangle for the AAS or ASA caseEXAMPLE1When you are given the measures of two angles and one side of a triangle, why does it not matter whether the given side is the one included between the two angles?It does not matter since you are given the measures of any two angles, you can always find the third angle measure.Key Question7Essential Understandings

What are the possible triangles for the SSA case?8Solve the SSA case with one solutionEXAMPLE2SOLUTION3. Write the Law of Sine proportion2. Draw a picture 5. Write the Law of Sine proportion9Examine the SSA case with no solutionEXAMPLE3SOLUTION2. Draw a picture What will happen if you try to solve the triangle by applying the law of sines and using your calculator?Write the Law of Sine proportion10Solve the SSA case with two solutionsEXAMPLE4SOLUTION3. Write the Law of Sine proportion2. Draw a picture 5. Write the Law of Sine proportion5. Write the Law of Sine proportion11VocabularyArea of Triangle:

12Write and Solve a real Use trig to find area of triangleEXAMPLE4KIS Vegetable Garden Esther and Frederick are setting up a triangular vegetable garden at KIS. They lay off lengths of 15ft and 11ft for two sides of the garden with a 62 angle between these two sides, what will be the area of the garden?1. Draw a picture SOLUTION13Lesson 9.5 Homework:Practice BPractice C Honors14