Trigonometry

Lesson:

Here you will be solving Oblique Triangles. These are triangles that have no right angles. As standard notation, the angles of a triangle are labeled as A, B, and C and their opposite sides as a, b, and c.

To solve an oblique triangle, you need to know the measure of at least one side and any two other parts of the triangle - either two sides, two angles, or one angle and one side. There are 4 cases that this applies to:

- Two angles and any side (AAS or ASA)

- Two sides and an angle opposite one of them (SSA)

- Three sides (SSS)

- Two sides and their included angle (SAS)

The first two cases can be solved using the Law of Sines.

Example 1:

Given Two Angles and One Side - AAS

For this triangle, Angle C = 102.3°, B = 28.7°, and side b = 27.4’

Find the remaining angle and sides.

By the law of sines you have:

a/sin 49° = b/sin 28.7° = c/sin 102.3°

Solution:

Using b = 27.4 produces a = 27.4/sin 28.7°(sin 49°) = 43.06’ and c = 27.4/sin 28.7°(sin 102.3°) = 55.75’.

A = 180° - B - C = 180° - 28.7 - 102.3° = 49.0°.