In this problem, you apply principles in trigonometry. Since it is not mentioned, you will not assume that the triangle is a special triangle such as the right triangle. Hence, you cannot use Pythagorean formulas. The only equations you can use is the Law of Sines and Law of Cosines.
For finding side a, you can answer this easily by the Law of Cosines. The equation is
a2=b2 +c2 -2bccosA
a2 = 11^2 + 8^2 -2(11)(8)(cos54)
a2 = 81.55
a = √81.55
a = 9
Then, we use the Law of Sines to find angles B and C. The formula would be
a/sinA = b/sinB = c/sinC
9/sin54° = 11/sinB
B = 80.4°
9/sin54° = 8/sinC
C = 45.6°
The answer would be: a ≈ 9, C ≈ 45.6, B ≈ 80.4
The real distance fro the shop to the store is 24 km
<em><u>Solution:</u></em>
Given that, Jakes map shows the distance from the bake stars cafe to the restaurant supply store as 3 centimeter
Scale of the map is 1 centimeter to 8 kilometers
Therefore, scale is:

Let "x" be the real distance from the shop to the store
Then by proportion, we get,

Thus real distance fro the shop to the store is 24 km