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  • Coterminal Angles

    In these lessons, we will look at angles at standard position and coterminal angles. An angle is said to be in standard position if it is drawn on the Cartesian plane (x-y plane) on the positive x-axis and turning counter-clockwise (anti-clockwise). The initial side of an angle is the ray where the measurement of an angle starts. The terminal side…

  • Law of Cosines: Given three sides

    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…

  • Law of Cosines / Cosine Rule

    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…

  • Law of Sines – No Solution

    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.…

  • Law of Sines – Ambiguous Case

    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…

  • Law of Sines: Given Two Angles And One Side

    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 =…

  • Law of Sines

    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…

  • Applications Of Trigonometry

    Hints On Solving Word Problems Or Applications Of Trigonometry: If no diagram is given, draw one yourself. Mark the right angles in the diagram. Show the sizes of the other angles and the lengths of any lines that are known Mark the angles or sides you have to calculate. Consider whether you need to create…

  • Real-Life Examples of Trigonometry

    Trigonometry has many real-life examples used broadly. Let’s get a better idea of trigonometry with an example. A boy is standing near a tree. He looks up at the tree and wonders “How tall is the tree?” The height of the tree can be found without actually measuring it. What we have here is a…

  • Tangent Ratio Problems

    In these lessons, we will learn how to find angles and sides using the tangent ratio and how to solve word problems using the tangent ratio. Hints on solving trigonometry problems: If no diagram is given, draw one yourself. Mark the right angles in the diagram. Show the sizes of the other angles and the…

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