given a triangle with sides measuring 18 inches,21 inches 14 inches find the measure of the anglewith the greatest ​

ANSWER[tex]A = 80.98 \degree[/tex]EXPLANATIONThe 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.