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* 24 * 30* \cos 130^\circ`

`$a^(2)=576+900-1440* (-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.