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,

$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$

Plug the given values.

$\frac{\sin35\degree}{a}=\frac{\sin108\degree}{74}=\frac{\sin37\degree}{c}$

Consider the equation

$\begin{gathered} \frac{\sin35\degree}{a}=\frac{\sin108\degree}{74} \\ a=\sin35\degree\frac{74}{\sin108\degree}\cdot \\ =44.6 \end{gathered}$

Consider the equation

$\frac{\sin108\degree}{74}=\frac{\sin37\degree}{c}$

Then

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