Please i need some help Solve the triangle ABC if the triang

Please i need some help

Solve the triangle ABC, if the triangle exists. B = 35 degree 42\' a = 38.6 b = 29.5 Select the correct choice below and fill in the answer boxes within the choice. A. There is only 1 possible solution for the triangle. The measurements for the remaining angles A and C and side c are as follows. m angle A = degree \' m angle C = degree \' m angle C = degree \' (Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed.) The length of side c = (Round to the nearest tenth as needed.) B. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. m angle A = degree \' m angle C = degree \' m angle C = degree \' (Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed.) The length of side c = (Round to the nearest tenth as needed.) The measurements for the solution with the shorter side c are as follows. m angle A = degree \' m angle C = degree \' m angle C = degree \' (Simplify your answer. Round to the nearest degree as needed. Round to the nearest minute as needed.) The length of side c = (Round to the nearest tenth as needed.) C. There are no possible solutions for this triangle.

Solution

A, B, and C are the angles of the triangle.
a is the length of the side opposite angle A.
b is the length of the side opposite angle B.
c is the length of the side opposite angle C.

Since there are 60 minutes in one degree, 42 min = 42/60 deg = .7deg, so B = 35.7 deg and sin B = sin 35.7 = 0.58354121

By the law of sines, sin B / b = sin A / a, so sin A = a sin B / b = ((38.6)(0.58354)) / 29.5 = 0.763547254
Then A = 49.777921902668 deg or A = 130.222078097 deg

The sum of the angles of a triangle is 180 deg, so A + B + C = 180 and C = 180 - A - B.

If A = 49.777921902668 deg then C = 180 - 49.777921902668 - 35.7 = 180 -85.4779219 =94.5220781 deg and sin C = 0.996887
Use the law of sines again.
sin B / b = sin C / c, or c = b sin C / sin B = ((29.5)(0.996887)) / 0.58354121 =50.396040

If A =130.222078097 deg then C = 180 - 130.222078097- 35.7 = 180 - 165.922078 = 14.0779 deg and sin C = 0.2432412692
By the law of sines
sin B / b = sin C / c, or c = b sin C / sin B = ((29.4)(.0.2432412692)) /0.58354121 = 12.2549927785

There are two possible solutions for triangle ABC
Solution 1 ---
A = 58.0 deg B = 35.7 deg C = 94.5220781 deg
a = 38.6 b = 29.5 c = 50.396040

Solution 2 ---
A = 130.222078097 deg B = 35.7 deg C = 14.0779deg
a = 38.6 b = 29.5 c = 112.2549927785