Answer:
∠B ≈ 50.9°
Step-by-step explanation:
The area formula for a triangle can be used to find the missing angle.
Area formula
We don't want confusion between A for area and angle A, so we define Q as the area of the triangle with sides a, c, and included angle B. In this scenario, 'a' represents side BC (opposite angle A), and 'c' represents side AB (opposite angle C).
Q = (1/2)ac·sin(B)
Unknown angle
Solving for B, we have ...
2Q/(ac) = sin(B)
B = arcsin(2Q/(ac)
B = arcsin(2(64)/(11(15)) = arcsin(128/165)
∠B ≈ 50.9°
