Question

Find the solutions for a triangle with a =11.4, b =13.7, and c =12.2.

Answer 1

To simplify the answer above this one, it is

C) A=51.8 B=70.9 C=57.3

Explanation:

I got it right on edge

Answer 2

The solutions for the triangle are: ∠A = 51.833...° , ∠B = 70.880...° and ∠C = 57.286...°

Explanation

For finding the unknown angles, we need to use Cosine rule. The formulas are...

`cos A = (b^2+c^2-a^2)/(2bc) \\ \\ cos B= (a^2+c^2-b^2)/(2ac)\\ \\ cos C= (a^2+b^2-c^2)/(2ab)`

Given that the length of three sides of the triangle as :
`a= 11.4, b= 13.7` and
`c=12.2`

Thus,

`cosA= ((13.7)^2+(12.2)^2 -(11.4)^2)/(2(13.7)(12.2)) \\ \\ cosA= (206.57)/(334.28) \\ \\ cosA= 0.61795... \\ \\ A= cos^-^1 (0.61795...)= 51.833... degree\\ \\ \\ \\  cos B= ((11.4)^2+(12.2)^2 -(13.7)^2)/(2(11.4)(12.2))\\ \\ cos B= (91.11)/(278.16) \\ \\ cos B= 0.3275...\\ \\ B= cos^-^1 (0.3275...)= 70.880... degree \\ \\ \\ \\ cos C= ((11.4)^2+(13.7)^2 -(12.2)^2)/(2(11.4)(13.7))\\ \\ cos C= (168.81)/(312.36) \\ \\ cos C= 0.54043...\\ \\ C= cos^-^1 (0.54043...)= 57.286... degree`