Answer:
A=98.05°, B= 40°, C= 41.95, a=38.5, b = 25, c = 26 ....
Step-by-step explanation:
According to the law of sine:
a / sin(A) = b / sin(B) = c / sin(C)
or you can also write it as:
sin(A) / a = sin(B) / b = sin(C) / c
We have:
B = 40°, b = 25, c = 26
We will use sin(B) / b = sin(C) / c to find angle C
sin(B) / b = sin(C) / c
Substitute the values in the rule:
sin(40)/25 = sin(C)/26
Multiply both sides by 26.
26*sin(40)/25 = sin(C)
26* 0.642788/25 = sin(C)
16.712488/25= sin(C)
0.66849952= sin(C)
sin−1(0.66849952)= C
41.95 degrees = C
Now we know that A+B+C=180°
Therefore put the values in the equation:
A+40+41.95=180°
A+81.95=180°
A=180°-81.95°
A=98.05°
Now take first two elements of sine rule:
a / sin(A) = b / sin(B)
a/sin(98.05°)= 25/sin(40°)
a=25*sin(98.05°)/sin(40°)
a=25(0.9901)/0.64278
a=24.7525/0.64278
a= 38.5
There fore
A=98.05°, B= 40°, C= 41.95, a=38.5, b = 25, c = 26 ....
