Question

Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. a=9,b=3,A=50∘Selected the correct choice below and, if necessary, fil in the answer boxes to complete your choice; (Round side lengths to the nearest tenth and angle measurements to the nearest dogree as needed) A. There is only one possible solution for the triangle. The measurements for the remaining side c and angles Band C are ns folows. B≈ B. There are two possible solutions for the triangle. The measurements for the solution with the the smaller angle B are as follows. B1​ 라 The measurements for the solution with the the larger angle B are as follows. B2​≈ : C2​≈ : c2​≈ c. There ace no possible solutions for this triangle. Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all. Solve each triangle that results. a=11,b=13,A=53∘ Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (Round side lengths to the nearest tenth and angle measurements to the nearest degree as needed.) A. There is only one possible solution for the triangle. The measurements for the remaining side C and angles Band C are as follows. B≈c≈;c≈ B. There are two possible solutions for the thangle. The measurements for the solution with the the smaller angle 8 are as follows. B1​≈ The measurements for the solution with the the larger angle B are as follows. B2​≈C2​≈ c. There are no possible solutions for this triangle.

Answer 1

Triangle 1:
Given: a = 9, b = 3, A = 50°
To determine the number of possible triangles, we can use the Law of Sines. Let's calculate the value of sin(B):

sin(B) = (b / a) * sin(A)
sin(B) = (3 / 9) * sin(50°) ≈ 0.1908

Since sin(B) is less than 1, there is only one possible solution for the triangle.

Using the Law of Sines, we can find the remaining side and angles:
c ≈ (b / sin(B)) ≈ (3 / 0.1908) ≈ 15.727
B ≈ arcsin((b * sin(A)) / a) ≈ arcsin((3 * sin(50°)) / 9) ≈ 23.746°
C ≈ 180° - A - B ≈ 106.254°

The measurements for the triangle are:
B ≈ 23.7°
C ≈ 106.3°
c ≈ 15.7

Therefore, the correct choice is A.

Triangle 2:
Given: a = 11, b = 13, A = 53°
Let's calculate the value of sin(B):

sin(B) = (b / a) * sin(A)
sin(B) = (13 / 11) * sin(53°) ≈ 0.9561

Since sin(B) is greater than 1, there are no possible solutions for this triangle.

Therefore, the correct choice is C.

So, for the given measurements:
Triangle 1 has one possible solution.
Triangle 2 has no possible solutions.