Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Trigonometry
Right-Angled Triangles
What is Right-Angled Triangles?
Triangles containing an angle of ninety degrees, in which each acute angle is linked to two of the three sides by the ratios sine, cosine and tangent: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse and tangent is opposite over adjacent. The labels opposite and adjacent are defined relative to a chosen reference angle and swap when the other acute angle is chosen, while the hypotenuse, opposite the right angle, never changes. These ratios, with Pythagoras' theorem, solve two-dimensional problems including shortest distances, angles of elevation and depression, and bearings.
This definition is part of the Trigonometry chapter in Cambridge O Level Mathematics (Syllabus D).
Questions students ask about Right-Angled Triangles
How do you decide between Pythagoras, SOHCAHTOA, the sine rule and the cosine rule?
Ask what kind of triangle you are looking at before writing any formula. A right angle with three lengths involved means Pythagoras; a right angle with an angle involved means sine, cosine or tangent. With no right angle, a side paired with the angle opposite it starts the sine rule; two sides with the angle between them, or three sides, start the cosine rule. A solid must first be cut into flat right-angled triangles.