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how did it come to 9 for B1? it's for solving The Ambiguous Case SSA for triangle.

how did it come to 9 for B1? it's for solving The Ambiguous Case SSA for triangle.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.1: Angles
Problem 3E
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how did it come to 9 for B1? it's for solving The Ambiguous Case SSA for triangle.

11/18/23, 11:52 PM 6-01-Vida Lumod The second possibility, B₂ 171°, is ruled out because A = 40°, making A + B₂ > 180°. Using B₁90, calculate C. Use the fact that the sum of the measures of the angles of any triangle is 180°. A+B+C = 180° Now we can determine side c using the Law of Sines. a sin A C= 180° - A-B₁180° -40° -9° 4 sin 40 = с sin C = с sin 131° C≈ 4.7 (Round to the nearest tenth.) There is one triangle and the solution is B 9°, C≈ 131°, and c≈ 4.7. YOU ANSWERED: 0.1607 Apply the Law of Sines. 41 131 Substitute the known values. Multiply both sides by sin 131° to solve for c.
Transcribed Image Text:11/18/23, 11:52 PM 6-01-Vida Lumod The second possibility, B₂ 171°, is ruled out because A = 40°, making A + B₂ > 180°. Using B₁90, calculate C. Use the fact that the sum of the measures of the angles of any triangle is 180°. A+B+C = 180° Now we can determine side c using the Law of Sines. a sin A C= 180° - A-B₁180° -40° -9° 4 sin 40 = с sin C = с sin 131° C≈ 4.7 (Round to the nearest tenth.) There is one triangle and the solution is B 9°, C≈ 131°, and c≈ 4.7. YOU ANSWERED: 0.1607 Apply the Law of Sines. 41 131 Substitute the known values. Multiply both sides by sin 131° to solve for c.
We solve an SSA triangle using the Law of Sines. The Law of Sines states that if A, B, and C are the measures of the angles of a triangle, a с and a, b, and c are the lengths of the sides opposite these angles, then b sin B sin A sin C Begin solving the triangle by using the Law of Sines to determine the angle B. a sin A 4 sin 40° = b sin B 1 sin B sin B 0.1607 (Round to four decimal places.) There are two angles B, 0° <B<180°, for which sin B≈ 0.1607. B₁ ≈ 9 (Type the smaller angle rounded to the nearest degree.) = A+B+C = 180° Apply the Law of Sines. 0 Substitute the known values. O B₂ ≈ 171 (Type the larger angle rounded to the nearest degree.) Cross multiply, and solve for sin B. https://tdx.acs.pearsonprd.tech/api/v1/print/highered sin C с 11/18/23, 11:52 PM 6-01-Vida Lumod The second possibility, B₂ 171°, is ruled out because A = 40°, making A+ B₂ >180°. Using B₁9°, calculate C. Use the fact that the sum of the measures of the angles of any triangle is 180°. C= 180° - A-B₁ 180° -40° -9° Now we can determine side c using the Law of Sines. a sin A 4 Apply the Law of Sines. 131 = O = 1/2
Transcribed Image Text:We solve an SSA triangle using the Law of Sines. The Law of Sines states that if A, B, and C are the measures of the angles of a triangle, a с and a, b, and c are the lengths of the sides opposite these angles, then b sin B sin A sin C Begin solving the triangle by using the Law of Sines to determine the angle B. a sin A 4 sin 40° = b sin B 1 sin B sin B 0.1607 (Round to four decimal places.) There are two angles B, 0° <B<180°, for which sin B≈ 0.1607. B₁ ≈ 9 (Type the smaller angle rounded to the nearest degree.) = A+B+C = 180° Apply the Law of Sines. 0 Substitute the known values. O B₂ ≈ 171 (Type the larger angle rounded to the nearest degree.) Cross multiply, and solve for sin B. https://tdx.acs.pearsonprd.tech/api/v1/print/highered sin C с 11/18/23, 11:52 PM 6-01-Vida Lumod The second possibility, B₂ 171°, is ruled out because A = 40°, making A+ B₂ >180°. Using B₁9°, calculate C. Use the fact that the sum of the measures of the angles of any triangle is 180°. C= 180° - A-B₁ 180° -40° -9° Now we can determine side c using the Law of Sines. a sin A 4 Apply the Law of Sines. 131 = O = 1/2
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