Question

Consider a triangle ABC like the one below. Suppose that =B108°, =C37°, and =b74. (The figure is not drawn to scale.) Solve the triangle.Round your answers to the nearest tenth. If there is more than one solution, use the button labeled "or".

Answer 1

Given:

B = 108 degrees, C = 37 degrees, b = 74

Required: Values of a, A and c.

Explanation: Since the sum of angles of a triangle is 180 degrees,

`\begin{gathered} m\angle A+m\angle B+m\angle C=180\degree \\ m\angle A+108\degree+37\degree=180\degree \\ m\angle A=35\degree \end{gathered}`

By using the sine Laws,

`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`

Plug the given values.

`(\sin35\degree)/(a)=(\sin108\degree)/(74)=(\sin37\degree)/(c)`

Consider the equation

`\begin{gathered} (\sin35\degree)/(a)=(\sin108\degree)/(74) \\ a=\sin35\degree(74)/(\sin108\degree)\cdot \\ =44.6 \end{gathered}`

Consider the equation

`(\sin108\degree)/(74)=(\sin37\degree)/(c)`

Then