SOLUTION: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse. cos(B) = 4/5, a = 38 b= c= Thanks in ad

Algebra ->  Trigonometry-basics -> SOLUTION: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse. cos(B) = 4/5, a = 38 b= c= Thanks in ad      Log On


   

Question 1129880: Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
cos(B) = 4/5, a = 38

b=
c=

Thanks in advance...
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Find the lengths of the missing sides if side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.
cos(B) = 4/5, a = 38
:
Draw a right triangle ABC, label the side opposite the angle as a, b, c
:
a side is adjacent to angle B, therefore
38%2Fc = Cos(B)
38%2Fc = 4/5
4c = 38 * 5
4c = 190
c = 190/4
c = 47.5 is the hypotenuse
:
Find b
Find angle B
cos%5E-1%28B%29 = 4%2F5
B = 36.87
sin(36.87) = b%2F47.5
b = 47.5 * sin(36.87)
b = 28.5