Question

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

Answer 1

its d, A=44 degrees B=56 degrees C=16.1

Explanation:

Answer 2

`\large \boxed{\angle A = 51.83 ^(\circ); \, \angle B = 70.88 ^(\circ); \, \angle C = 57.29 ^(\circ)}`

Explanation:

You use the Law of Cosines when you know all three sides and want to find the angles of a triangle.

For example, if you want to find ∠A, you use the formula

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

1. ∠ A

`\begin{array}{rcl}\cos A &=& (b^(2) + c^(2) - a^(2))/(2bc)\\\\& = & (13.7^(2) + 12.2^(2) - 11.4^(2))/(2* 13.7 * 12.2)\\\\& = & (187.69 + 148.84 - 129.96)/(334.28)\\\\&=& (206.57)/(334.28)\\\\& = & 0.6180\\A& = & \arccos 0.6180\\& = & \mathbf{51.83 ^(\circ)}\\\end{array}`

2. ∠B

`\begin{array}{rcl}\cos B &=& (a^(2) + c^(2) - b^(2))/(2ac)\\\\& = & (11.4^(2) + 12.2^(2) - 13.7^(2))/(2* 11.4 * 12.2)\\\\& = & (129.96 + 148.84 - 187.69)/(278.16)\\\\&=& (91.11)/(278.16)\\\\& = & 0.3275\\B& = & \arccos 0.3275\\& = & \mathbf{70.88 ^(\circ)}\\\end{array}`

3. ∠C

`\begin{array}{rcl}\cos C &=& (a^(2) + b^(2) - c^(2))/(2bc)\\\\& = & (11.4^(2) + 13.7^(2) - 12.2^(2))/(2* 11.4 * 13.7)\\\\& = & (129.96 + 187.69 - 148.84)/(312.36)\\\\&=& (168.81)/(312.36)\\\\& = & 0.5404\\C& = & \arccos 0.5404\\& = & \mathbf{57.29 ^(\circ)}\\\end{array}\\\text{The three angles are $\large \boxed{\mathbf{\angle A = 51.83 ^(\circ); \, \angle B = 70.88 ^(\circ); \, \angle C = 57.29 ^(\circ)}}$}`