a = 6.2
Solution:
Given ABC is triangle.
AC = b = 8, BA = c = 11, ∠A = 32.2°
BC = a
To find the length of a:
Law of cosines:
[tex]a^{2}=b^{2}+c^{2}-2 b c \cdot \cos A[/tex]
[tex]a^{2}=8^2+11^{2}-2 \times 8 \times 11 \cdot \cos 32.2^\circ[/tex]
[tex]a^{2}=64+121-174 \cdot \cos 32.2^\circ[/tex]
[tex]a^{2}=185-174 (0.8461)[/tex]
[tex]a^{2}=185-147.221[/tex]
[tex]a^{2}=37.779[/tex]
Taking square root on both sides of the equation.
a = 6.1464
a = 6.2
The length of BC is 6.2.
