Option B:
BC = 49 feet
Solution:
Given m∠A = 130°,
AB = c = 30 feet
AC = b = 24 feet
BC = a = ?
Law of cosines:
[tex]a^{2}=b^{2}+c^{2}-2 b c \cos A[/tex]
Substitute the given values in the formula.
[tex]$a^{2}=24^{2}+30^{2}-2\times 24 \times 30\times \cos 130^\circ[/tex]
[tex]$a^{2}=576+900-1440\times (-0.64)[/tex]
[tex]$a^{2}=1476+921.6[/tex]
[tex]$a^{2}=2397.6[/tex]
Taking square root on both sides, we get
a = 48.96
a = 49 feet
BC = 49 feet
Option B is the correct answer.
