ANSWER
[tex]A = 80.98 \degree[/tex]
EXPLANATION
The angle with the greatest measure corresponds to the longest:
Since we know the three side lengths, we use the cosine rule to obtain;
[tex] {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos(A) [/tex]
where a=21, b=18 and c=14
[tex] {21}^{2} = {18}^{2} + {14}^{2} - 2 \times 18 \times 14\cos(A) [/tex]
[tex]44 1= 324+ 196 - 504\cos(A) [/tex]
[tex]44 1= 520 - 504\cos(A) [/tex]
[tex]44 1 - 520 = - 504\cos(A) [/tex]
[tex] - 79 = - 504\cos(A) [/tex]
[tex]\cos(A) = 0.1567[/tex]
[tex]A = \cos ^{ - 1} (0.1567) = 80.98 \degree[/tex]
correct to the nearest hundredth.
