Answer: option c.
Step-by-step explanation:
To find AB you can use this trigonometric identity:
[tex]tan\alpha=\frac{opposite}{adjacent}[/tex]
In this case:
[tex]\alpha=\angle A=48.8\°\\opposite=BC=1.6in\\adjacent=AC[/tex]
Substituting values and solving for AC, we get:
[tex]tan(48.8\°)=\frac{1.6in}{AC}\\\\AC=\frac{1.6in}{tan(48.8\°)}\\\\AC=1.4in[/tex]
To find AB you can use the Pythagorean Theorem:
[tex]c^2=a^2+b^2[/tex]
Where "c" is the hypotenuse and "a" and "b" are the legs of the triangle.
In this case:
[tex]c=AB\\b=AC=1.4in\\\\a=BC=1.6in[/tex]
Substituting values and solving for AB, we get:
[tex]AB^2=(1.6in)^2+(1.4in)^2\\\\AB=\sqrt{(1.6in)^2+(1.4in)^2}\\\\AB=2.1in[/tex]
Since the sum of the interior angles of a triangle is 180 degrees, we know that ∠B is:
[tex]\angle B=180\°-\angle A-\angle C\\\\\angle B=180\°-48.8\°-90\°\\\\\angle B=41.2\°[/tex]
