Question

Given a triangle with sides measuring 18 inches, 21 inches, and 14 inches find the measure of the angle with the greatest measure.
a. about 76
c. about 84
b. about 81
d about 90
Please select the best answer from the choices provided

Answer 1

B :81 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;
{a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos(A)
where a=21, b=18 and c=14
{21}^{2} = {18}^{2} + {14}^{2} - 2 \times 18 \times 14\cos(A)
44 1= 324+ 196 - 504\cos(A)
44 1= 520 - 504\cos(A)
44 1 - 520 = - 504\cos(A)
- 79 = - 504\cos(A)
\cos(A) = 0.1567
A = \cos ^{ - 1} (0.1567) = 80.98 \degree