How do you solve the triangle given ∠B = 151°, ∠C = 7°, a = 31?

2 Answers
Dec 23, 2016

b= 40.12, c=10.09 and #angle A#= #22^o#

Explanation:

The triangle would appear to like in the figure given below. Angle A would be 180- (151+7) = #22^o#
enter image source here
Using sine formula,

#sin22 /31 = sin 151 /b = sin 7 /c#

b= #31* sin 151 /sin22#= 40.12

c= #31* sin7 / sin 22# =10.09

Dec 23, 2016

Subtract #angle B and angle C# from #180^@#, to find #angle A#, then use The Law of Sines to find the lengths of sides "b" and "c".

Explanation:

#angle A = 180^@ - angle B - angle C#

#angle A = 180^@ - 151^@ - 7^@#

#angle A = 22^@#

Use The Law of Sines

#a/sin(A) = b/sin(B) = c/sin(C)#

#b = asin(B)/sin(A)#

#b = 31sin(151^@)/sin(22^@)#

#b~~ 40#

#c = asin(C)/sin(A)#

#c = 31sin(7^@)/sin(22^@)#

#c~~ 10#