Use the low of Cosines to solve the given triangle.Round your answer to two decimal places.
A = 51,b = 21,c = 68

A)A ≈ 30.37°,B ≈ 12.02°,C ≈ 137.61°
B)A ≈ 30.37°,B ≈ 137.61°,C ≈ 12.02°
C)A ≈ 12.02°,B ≈ 30.37°,C ≈ 137.61°
D)A ≈ 137.61°,B ≈ 12.02°,C ≈ 30.37°
E)A ≈ 137.61°,B ≈ 30.37°,C ≈ 12.02°

Question

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 51,b = 21,c = 68
​
A)A ≈ 30.37°,B ≈ 12.02°,C ≈ 137.61°
B)A ≈ 30.37°,B ≈ 137.61°,C ≈ 12.02°
C)A ≈ 12.02°,B ≈ 30.37°,C ≈ 137.61°
D)A ≈ 137.61°,B ≈ 12.02°,C ≈ 30.37°
E)A ≈ 137.61°,B ≈ 30.37°,C ≈ 12.02°

Quizplus · Accepted Answer

Using the Law of Cosines:
cos(A) = (b^2 + c^2 - a^2)/(2bc)
cos(A) = (21^2 + 68^2 - 51^2)/(2*21*68)
cos(A) = 0.622
A = acos(0.622)
A ≈ 30.37°

Now using the Law of Sines:
sin(B)/b = sin(A)/a
sin(B)/21 = sin(30.37)/51
sin(B) = (21*sin(30.37))/51
B = asin((21*sin(30.37))/51)
B ≈ 12.02°

Finally, C = 180 - A - B
C ≈ 137.61°

Therefore, the answer is A)A ≈ 30.37°,B ≈ 12.02°,C ≈ 137.61°.

Use the Low of Cosines to Solve the Given Triangle