Respuesta :
use the Cosine Rule:
x^2 = 12^2 + 14^2 - 2*12*14 cos 112
x = 21.6
B is the correcct answer
x^2 = 12^2 + 14^2 - 2*12*14 cos 112
x = 21.6
B is the correcct answer
Answer:
Option B.
Step-by-step explanation:
Given information: AB=12 miles, BC=14 miles and ∠B=112°.
Using given information, we get
[tex]AB=c=12\text{ miles}[/tex]
[tex]BC=a=14\text{ miles}[/tex]
We need to find the value of CA or b.
Cosine formula:
[tex]b^2=a^2+c^-2ac\cos B[/tex]
Substitute a=14, c=12 and B=112.
[tex]b^2=(14)^2+(12)^-2(14)(12)\cos (112)[/tex]
[tex]b^2=196+144-336(-0.3746)[/tex]
[tex]b^2=340+125.8656[/tex]
[tex]b^2=465.8656[/tex]
Taking square root on both sides.
[tex]b=\sqrt{465.8656}[/tex]
[tex]b=21.5839[/tex]
[tex]b\approx 21.6[/tex]
Therefore, the correct option is B.
