in triangle ab, a =4, and m? c=30

Question

if the area of the triangle is 6,what is the length of side b?

Answer 1

AURORA, the triangle needs a 3-letter, all capitalized, name.

a = 4 is OK, meaning the length of a side labeled lower case a.

Apparently the measure of angle C is 30^o.  (C must be capitalized.)

 

The formula area = ½•ab•sinC can be used, so

6 = ½•4b•sinC can be used, so
6 = ½•4b•sin30^o and said sine has value ½

 

6 = 2b(½)  so b = 6.