Question

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

A = 55°, a = 12, b = 14

Answer 1

Answer on Question #53920 – Math – Trigonometry

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

A = 55°, a = 12, b = 14

Solution

By the Law of Sines

$$\frac {\sin A}{a} = \frac {\sin B}{b} \rightarrow \sin B = b \frac {\sin A}{a} \rightarrow \text{angle } B = \sin^ {- 1} \left(b \frac {\sin A}{a}\right).$$ $$B = \sin^ {- 1} \left(14 \frac {\sin 55{}^{\circ}}{12}\right) = 72.877{}^{\circ} \text{ or } 180{}^{\circ} - 72.877{}^{\circ} = 107.123{}^{\circ}.$$

A, B, C are angles of triangle, therefore angle

$$C = 180{}^{\circ} - (55{}^{\circ} + 72.877{}^{\circ}) = 52.123{}^{\circ} \text{ or } 17.877{}^{\circ}.$$

The length of side

$$c = a \frac {\sin C}{\sin A} = 12 \frac {\sin 52.123{}^{\circ}}{\sin 55{}^{\circ}} = 11.563 \text{ or } 12 \frac {\sin 17.877{}^{\circ}}{\sin 55{}^{\circ}} = 4.497.$$

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