Question

What is the answer, law of cosine for geometry

Answer 1

Option B:

BC = 49 feet

Solution:

Given m∠A = 130°,

AB = c =  30 feet

AC = b = 24 feet

BC = a = ?

Law of cosines:

$a^{2}=b^{2}+c^{2}-2 b c \cos A$

Substitute the given values in the formula.

$a^{2}=24^{2}+30^{2}-2\times 24 \times 30\times \cos 130^\circ$

$a^{2}=576+900-1440\times (-0.64)$

$a^{2}=1476+921.6$

$a^{2}=2397.6$

Taking square root on both sides, we get

a = 48.96

a = 49 feet

BC = 49 feet

Option B is the correct answer.