Grade 10 MATH Solving Oblique Triangle Applying Laws of Sines First Term (Term 1) Week 1 Revised k10

The lesson introduces oblique triangles as any triangle without a 90-degree angle, encompassing acute and obtuse triangles. It then defines the Law of Sines as a rule for solving oblique triangles by showing the relationship between a triangle's sides and the sines of its angles. The formula (sin A / a = sin B / b = sin C / c) is presented, emphasizing that angles and their opposite sides are always paired.

The video outlines three specific cases where the Law of Sines can be applied: SAA (Side-Angle-Angle), ASA (Angle-Side-Angle), and SSA (Side-Side-Angle), also known as the ambiguous case. Illustrations are provided for each case to help viewers identify the given information in a triangle.

An example demonstrates how to solve an oblique triangle given in the SAA case (side C=20, angle B=100°, angle C=50°). The first step is to find the missing angle A using the sum of angles in a triangle (180°). Then, the Law of Sines is applied to find the missing sides A and B through cross-multiplication and isolation of the unknown variable.

A second example illustrates solving an oblique triangle in the ASA case (angle A=25°, angle B=110°, side C=15). Similar to the SAA case, angle C is first determined using the sum of angles in a triangle. Subsequently, the Law of Sines is used to calculate the lengths of sides A and B.

The video delves into the SSA case, highlighting its ambiguous nature. An example with angle A=30°, side A=10, and side B=15 is used. It's explained that in the SSA case, there can be two possible solutions for the angles, leading to two different triangles. The calculation for angle B reveals two potential values (48.59° and 131.41°). Each of these values forms a valid triangle, making the case 'ambiguous'.

The lesson concludes by explaining how to determine whether an SSA case is ambiguous or not. If the given angle in an SSA scenario is acute, it is an ambiguous case, potentially yielding zero, one, or two solutions. However, if the given angle is obtuse, it is not an ambiguous case and typically has only one solution if the opposite side is greater than the adjacent side.