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7.1 Law of Sines Day 1 Do Now Let Triangle ABC be a right triangle where angle C is 90 degrees, angle B is 37.1 degrees, and side BC is 6.3 Solve the triangle.

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Presentation on theme: "7.1 Law of Sines Day 1 Do Now Let Triangle ABC be a right triangle where angle C is 90 degrees, angle B is 37.1 degrees, and side BC is 6.3 Solve the triangle."— Presentation transcript:

1 7.1 Law of Sines Day 1 Do Now Let Triangle ABC be a right triangle where angle C is 90 degrees, angle B is 37.1 degrees, and side BC is 6.3 Solve the triangle

2 Test Review Retakes by

3 Solving Triangles To solve a triangle means to find the lengths of all its sides and the measures of all its angles Weve solved right triangles previously

4 Oblique Triangles A triangle that is not a right triangle is considered oblique Oblique triangles can be solved if at least one side and any other 2 measures (length or angle) are known

5 Law of Sines Proof

6 Law of Sines In any triangle ABC, Where side a is opposite of angle A, etc

7 Law of Sines notes When solving triangles, there is a possibility that you can have one solution, two solutions, or no solution. This depends on the equations you set up – Remember, the range of sinx is [-1, 1]

8 Ex1 In triangle EFG, e = 4.56, E = 43deg, G = 57 deg Solve the triangle

9 Ex3 In Triangle QRS, q = 15, r = 28, Q = 43.6 deg Solve the triangle

10 Ex 4 In triangle XYZ, x = 23.5, y = 9.8, X = 39.7 deg Solve the triangle

11 Ex5 In triangle ABC, b = 15, c = 20, B = 29 deg Solve the triangle

12 Closure Solve the triangle ABC, if possible A = 131 deg, C = 23 deg, b = 10 HW: p.608 #1-15 odds

13 7.1 Law of Sines Day 2 Do Now In triangle ABC, B = 115deg, c = 45.6 yd, b = 23.8 yd. Solve the triangle

14 HW Review: p.608 #1-15

15 Ex2 In book

16 Area of a Triangle Using the law of sines, we can find the area K of a triangle

17 Ex6 A university landscaping architecture department is designing a garden for a triangular area in a dormitory complex. Two sides of the garden, formed by the sidewalks in front of buildings A and B, measure 172 ft and 186 ft respectively, and together form a 53 degree angle. The third side of the garden measures 160 ft. Find the area of the garden to the nearest square foot.

18 Closure Find the area of the triangle ABC given C = degrees, a = 1.5 m, b = 2.1 m HW: p.608 #17-31 odds


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