Trigonometry — NSW Year 10 Core Maths
Sine, cosine and tangent in right-angled triangles: unknown sides and angles, elevation and depression, and bearings. Five subtopics and 100 practice questions with worked solutions, aligned to NESA MA5-TRG-C-01 and MA5-TRG-C-02.
Trigonometry in NSW Year 10 Core
Trigonometry connects the angles of a right-angled triangle with the ratios of its sides. In Year 10 Core, students name the hypotenuse, opposite and adjacent sides, define sine, cosine and tangent, and use them with a calculator to find unknown sides and angles, working in degrees and minutes.
The five subtopics below start with the ratios, move on to finding angles and sides, and finish with applications: angles of elevation and depression, and bearings. Trigonometry is one of the 11 topics in NSW Year 10 Maths Core and sits within NESA's Measurement and Space strand (NESA outcomes MA5‑TRG‑C‑01 and MA5‑TRG‑C‑02). It builds on Pythagoras' theorem from Stage 4 and leads to the sine and cosine rules and three-dimensional problems in later study.
Subtopics
Trigonometry: common questions
What is SOH CAH TOA?
It is a memory aid for the three ratios: \(\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}\), \(\cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}\) and \(\tan\theta = \frac{\text{opposite}}{\text{adjacent}}\).
How do you find an angle using trigonometry?
Choose the ratio that uses the two sides you know, then use the inverse function on your calculator. For example, if \(\tan\theta = 3\), then \(\theta = \tan^{-1} 3 \approx 71^\circ 34'\). Make sure the calculator is in degree mode.
What is the difference between angles of elevation and depression?
An angle of elevation is measured upwards from the horizontal to an object above you; an angle of depression is measured downwards from the horizontal to an object below you. Both are measured from the horizontal, never from the vertical.
Which NESA outcomes cover Year 10 Core trigonometry?
Trigonometry sits in Stage 5 of the NSW Mathematics K–10 Syllabus (2022). The ratios and finding unknown sides and angles come under MA5‑TRG‑C‑01, and elevation, depression and bearing problems under MA5‑TRG‑C‑02.
What is a true bearing?
A true bearing gives a direction as a three-figure angle measured clockwise from north. For example, east is \(090^\circ\) and south-west is \(225^\circ\).