Question

Solve the right triangle shown in the figure BC = 1.6in< A=48.8 C =90

Answer 1

I think your answer is A

Answer 2

Drawing a diagram to represent the information you've given, the only angle we are missing is B.  We can find that by subtracting the two we're given from 180:
180 - 90 - 48.8 = 41.2
m∠B = 41.2°.
We can use the angles and the one side we're given to find the remaining sides.  Since we do not know the length of the hypotenuse, AB, we cannot use sine or cosine.  We must use tangent (the ratio for tangent is opposite/adjacent):
$\tan 41.2 = \frac{x}{1.6}$
Multiply both sides by 1.6:
$1.6 \tan 41.2 = x \\ 3.67 = x$
This is the length of side AC, which is opposite to angle B.
To find the length of AB we can use the Pythagorean Theorem:
$(1.6)^2+(3.67)^2=c^2 \\ 2.56+13.4689=c^2 \\ 16.0289=c^2 \\ \sqrt{16.0289} = \sqrt{c^2} \\ 4=c$
The length of side AC, the hypotenuse, is 4 inches.