Study Notes
Right angle trigonometry involves understanding the properties and relationships within right-angled triangles, including the Pythagorean theorem and trigonometric ratios.
- Right-Angled Triangle — a triangle with one angle equal to 90 degrees. Example: In triangle ABC, angle C is 90°.
- Hypotenuse — the longest side of a right-angled triangle, opposite the right angle. Example: In triangle ABC, if angle C is 90°, then side AB is the hypotenuse.
- Pythagorean Theorem — in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Example: If the sides are a, b, and c (hypotenuse), then c² = a² + b².
- Sine (sin) — a trigonometric ratio defined as the opposite side over the hypotenuse. Example: sin(θ) = opposite/hypotenuse.
- Cosine (cos) — a trigonometric ratio defined as the adjacent side over the hypotenuse. Example: cos(θ) = adjacent/hypotenuse.
- Tangent (tan) — a trigonometric ratio defined as the opposite side over the adjacent side. Example: tan(θ) = opposite/adjacent.
Exam Tips
Key Definitions to Remember
- A right-angled triangle has one angle of 90 degrees.
- The hypotenuse is the longest side in a right-angled triangle.
- Pythagorean Theorem: c² = a² + b².
- Sine (sin): opposite/hypotenuse.
- Cosine (cos): adjacent/hypotenuse.
- Tangent (tan): opposite/adjacent.
Common Confusions
- Mixing up the hypotenuse with other sides.
- Confusing sine, cosine, and tangent ratios.
Typical Exam Questions
- What is the length of the hypotenuse if the other sides are 3 cm and 4 cm? Answer: 5 cm (using Pythagorean theorem).
- Calculate sin(θ) if the opposite side is 5 cm and the hypotenuse is 13 cm. Answer: sin(θ) = 5/13.
- Find the length of the adjacent side if tan(θ) = 0.75 and the opposite side is 6 cm. Answer: 8 cm.
What Examiners Usually Test
- Ability to identify and label sides of a right-angled triangle.
- Application of the Pythagorean theorem to find missing sides.
- Use of trigonometric ratios to solve for unknown sides or angles.