Month: September 2022

Example:In triangle ABC, a = 9 cm, b = 10 cm and c = 13 cm. Find the size of the largest angle. Solution:The largest angle is the one facing the longest side, i.e. C. c2 = a2 + b2 – 2ab cos C = 0.067 ∠C = 86.2° How to use the cosine rule?One given SAS and… Continue reading Law of Cosines: Given three sides

In these lessons, we will learn: the Law of Cosines how to use the Law of Cosines when given two sides and an included angle how to use the Law of Cosines when given three sides how to proof the Law of Cosines how to solve applications or word problems using the Law of Cosine… Continue reading Law of Cosines / Cosine Rule

It is also possible that when given SSA, the triangle does not exists and the Law of Sines will indicate no solution. Law of Sine – Ambiguous Case (SSA) – No SolutionWhen given two sides and a non included angle (SSA) in a triangle, this is known as the ambiguous case for Law of Sines.… Continue reading Law of Sines – No Solution

We will now consider the situation when we are given two sides and one angle of a triangle. Ambiguous CaseIf you are given two sides and a non-included acute angle and the side facing the given angle is less than the other side, you would obtain two sets of answers. The solution is said to be ambiguous. Example:Solve… Continue reading Law of Sines – Ambiguous Case

We will first consider the situation when we are given 2 angles and one side of a triangle. Example:Solve triangle PQR in which ∠P = 63.5° and ∠Q = 51.2° and r = 6.3 cm.  Solution:First, calculate the third angle. ∠ R = 180° – 63.5° – 51.2° = 65.3° Next, calculate the sides. ∠ R =… Continue reading Law of Sines: Given Two Angles And One Side

In these lessons, we will learn the Law of Sines, how to use the Law of Sines when given two angles and one side, how to use the Law of Sines when given two sides and a non-included angle, about the ambiguous case when using the Law of Sines, about the “no solutions” case when… Continue reading Law of Sines