how did it come to 9 for B1? it's for solving The Ambiguous Case SSA for triangle.
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.
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
Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).
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