Homework SourseSolve the triangle ABC if the triangle exists A445 a86m b108
Solve the triangle ABC, if the triangle exists.
A=44.5
a=8.6m
b=10.8m
Select the correct choice below and fill in the answer boxes within the choice.
A.
There are 2 possible solutions for the triangle.
The measurements for the solution with the longer side c are as follows.
mB=
(Round to the nearest tenth as needed.)
mC=
(Round to the nearest tenth as needed.)
c=
(Round to the nearest tenth asneeded.)
The measurements for the solution with the shorter side c are as follows.
mB=
(Round to the nearest tenth as needed.)
mC=
(Round to the nearest tenth as needed.)
c=
(Round to the nearest tenth asneeded.)
B.
There is only 1 possible solution for the triangle.
The measurements for the remaining angles B and C and side c are as follows.
mB=
(Round to the nearest tenth as needed.)
mC=
(Round to the nearest tenth as needed.)
c=
(Round to the nearest tenth asneeded.)
C.
There are no possible solutions for this triangle.
| The measurements for the solution with the longer side c are as follows. | ||
| mB= (Round to the nearest tenth as needed.) | mC= (Round to the nearest tenth as needed.) | The length of side c= (Round to the nearest tenth asneeded.) |
| The measurements for the solution with the shorter side c are as follows. | ||
| mB= (Round to the nearest tenth as needed.) | mC= (Round to the nearest tenth as needed.) | The length of side c= (Round to the nearest tenth asneeded.) |
Solution
A = 44.5
a = 8.6
b = 10.8
since a > b sin A
hence, the triangle will have 2 solutions
a / sin A = b / sin B
8.6 / sin 44.5 = 10.8 / sin B
B = 61.7 degrees
C = 180 - (44.5+ 61.7) = 73.8 degrees
8.6 / sin 44.5 = c / sin 73.8
c = 11.8
finding 2nd solution
A = 44.5
B = 180 - 61.7 = 118.3 degrees
C = 17.2 degrees
8.6 / sin 44.5 = c / sin 17.2
c = 3.6
so, there are 2 possible solutions
measurements for longer side c are as follows
m angle B = 61.7
m angle C = 73.8
c = 11.8
measurements of shorter side c is as follows
m angle B = 118.3
m angle C = 17.2
c = 3.6
