Solve the triangle ABC, if the triangle exists. A = 44.5 degree a = 8.1 m b = 10
ID: 3026056 • Letter: S
Question
Solve the triangle ABC, if the triangle exists. A = 44.5 degree a = 8.1 m b = 10.7 m 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 B and C and side c are as follows. m angle B = degree m angle C = degree The length of side c = B. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. m angle B = degree m angle C = degree The length of side c = The measurements for the solution with the shorter side c are as follows. m angle B = degree m angle C = degree The length of side c = C. There are no possible solutions for this triangle.Explanation / Answer
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.
so A = 44.5 deg and sin A = sin 44.5 =0.7009092
By the law of sines, sin B / b = sin A / a, so sin B = b sin A / a = ((10.7)(0.7009092 )) / 8.1 =0.925892
Then B = 67.803247 deg or B = 112.196752 deg.
The sum of the angles of a triangle is 180 deg, so A + B + C = 180 and C = 180 - A - B.
If B = 67.803247 deg then C = 180 - 44.5 - 67.803247 =67.69675 deg and sin C = 0.9251882
Use the law of sines again.
sin B / b = sin C / c, or c = b sin C / sin B = ((10.7)(0.9251882)) / 0.925892 =10.691866
If B = 112.196752 deg then C = 180 - 44.5 - 112.196752 = 23.30324 deg and sin C =0.3955975
By the law of sines
sin B / b = sin C / c, or c = b sin C / sin B = ((10.7)(0.3955975)) /0.925892 = 4.5716922168
There are two possible solutions for triangle ABC
Solution 1 ---
A = 44.5 deg B = 67.803247 deg C = 67.69675 deg
a = 8.1 b = 10.7 c = 10.691866
Solution 2 ---
A = 44.5 deg B = 112.196752 deg C =23.30324 deg
a = 8.1 b = 10.7 c = 4.5716922168