In triangle ABC, if the length of side b is 3 centimeters and the measures of /_B and /_C are 45° and 60°, respectively, what is the length of side c to two decimal places?

1 Answer
Oct 18, 2016

3.67 cm

Explanation:

We need to use the law of sines, a/SinA = b/SinB = c/SinC

Substituting for hatB and hatC, we get 3/Sin45 = c/Sin60

Now convert the special angles: 3/(sqrt2/2) = c/(sqrt3/2)

Multiply both sides by sqrt3/2 to get c by itself and simplify:

c=(sqrt3/2) xx 3/(sqrt2/2)

c = (3sqrt3)/2/(sqrt2/2) Cancel out the denominators

=(3sqrt3)/(sqrt2) Multiply top and bottom by (sqrt2)

=(3sqrt6)/2. Now we can check our answer

3/(sqrt2/2) = (3sqrt6/2)/(sqrt3/2)

sqrt6/sqrt3=sqrt2

3/(sqrt2/2) = 3/(sqrt2/2)

So, c=(3sqrt6)/2≈ 3.67 cm