The length of AB is 31 yd.
Solution:
Given data:
The side opposite to angle A is "a" = 22 yd
The side opposite to angle B is "b" = 26 yd
The side opposite to angle C is "c" = AB
Angle C = 80°
To find the length of AB:
Using cosine formula,
[tex]c^2=a^2+b^2-2ab \cdot \cos C[/tex]
Substitute the given values in the formula, we get
[tex]c^2=22^2+26^2-2(22)(26)\cdot \cos 80^\circ[/tex]
[tex]c^2=484+676-1144\cdot \cos 80^\circ[/tex]
[tex]c^2=1160-1144\cdot (0.1736)[/tex]
[tex]c^2=1160-198.5984[/tex]
[tex]c^2=961.4016[/tex]
Taking square root on both sides, we get
c = 31
AB = 31 yd
The length of AB is 31 yd.
