α =46º
1) Let's start by gathering the data:
S = 15 u²
a= 5.5
b= 7.5
Sketcing out:
2) One of the formulas to find out the area of a triangle is:

Plugging the given data into the formula we have:

2.2) Since we want to know the measure of that angle, then let's make use of the arcsine of (0.72)

3) Hence, the missing acute angle is α =46º (rounded off to nearest whole number)