Question

Math Wiz help! (law of cosines)

In aΔABC, if ∠B = 60° and the ratio of two sides is a : c = 2 : √3 + 1, then ∠A= ____.


In triangle ABC, a = 3, b = 5, and c = 7. Find the measure of B.

Answer 1

a] Using sine rule:
a/sin A=c/sin C
thus we can rewrite this as:
a/c=sin A/sinC
given that the ratio of a:c=2:√3+1 and C=60
thus
2/(√3+1)=sin A/sin 60
sin A=(2sin 60)/(√3+1)
sin A=0.63398
A=arcsin 0.63398~39.35°

b] In triangle ABC, a = 3, b = 5, and c = 7. Find the measure of B.
the value of B will be found using cosine rule as follows:
b²=a²+c²+2acCosB
thus
5²=3²+7²-2×3×7cos B
thus
25=9+49-42cos B
-33=-42cosB
cosB=0.7857
B=arccos 0.7857
B=38.21°