Law of Sines - Solving Oblique Triangle

Summary

This video explains how to use the Law of Sines to solve oblique triangles. It covers the formula, how to identify the parts of a triangle, and walks through a complete example to find missing angles and side lengths.

Highlights

Introduction to the Law of Sines and its Formula00:00:02

The video introduces the Law of Sines, primarily used for solving oblique triangles. It presents the formula: a/sin A = b/sin B = c/sin C, and its inverse, where 'a', 'b', 'c' are side lengths and 'A', 'B', 'C' are their opposite angles.

Problem Introduction and Listing Given Information00:01:10

An example problem is introduced: a triangle ABC with angle B = 141 degrees, angle C = 23 degrees, and side a = 9 units. The goal is to find angle A, side B, and side C. The presenter lists all known and unknown angles and sides.

Calculating Missing Angle A00:03:21

The first step is to find angle A. Since the sum of angles in a triangle is 180 degrees, angle A is calculated as 180 - (angle B + angle C). Plugging in the given values, angle A is found to be 16 degrees.

Solving for Side B using the Law of Sines00:04:56

To find side B, the Law of Sines a/sin A = b/sin B is used. Given values are substituted: 9/sin 16 = B/sin 141. The equation is then cross-multiplied and solved for B, resulting in B being approximately 20.5 units.

Solving for Side C using the Law of Sines00:09:11

Finally, to find side C, the Law of Sines a/sin A = c/sin C is applied. The known values are substituted: 9/sin 16 = C/sin 23. This equation is also cross-multiplied and solved for C, yielding an approximate value of 12.8 units for C.