Answer:
AC = 0.47 mi
BC = 0.51 mi
Step-by-step explanation:
Notice that we are in the case of an acute triangle for which we know two angles ( < A = 63 and < B = 56) and one side (AB = 0.5).
We can find the measure of the third angle using the property of addition of three internal angles of a triangle:
< A + < B + < C = 180
63 + 56 + < C = 180 degrees
< C = 180 - 63 - 56 = 61 degrees.
Now we use the law of sines to find the length of sides AC and BC:
[tex]\frac{0.5}{sin(61)} =\frac{AC}{sin(56)}\\AC=\frac{0.5*sin(56)}{sin(61)} \\AC\approx 0.4739\,\,\,mi[/tex]
which can be rounded to two decimals as:
AC = 0.47mi
For side BC we use:
[tex]\frac{0.5}{sin(61)} =\frac{BC}{sin(63)}\\BC=\frac{0.5*sin(63)}{sin(61)} \\BC\approx 0.509\,\,\,mi[/tex]
which can be rounded to two decimals as:
BC = 0.51 mi
