Question

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

Answer 1

`A = 80.98 \degree`

Step-by-step 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 * 18 * 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`

correct to the nearest hundredth.