Free Year 9 Trigonometric ratios Practice | Skillo
Skillo provides free Year 9 NAPLAN Trigonometric ratios practice (AC9M9SP01) for Australian students. No signup, no email, no credit card. Practice questions aligned with the ACARA Australian Curriculum v9.0 strand. Open and start in 10 seconds.
Year 9 students sitting their final NAPLAN need to be confident with trigonometric ratios. Recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity. Skillo has targeted practice questions for this exact skill, mapped to the Australian Curriculum v9.0, free and ready to go.
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What does the Year 9 NAPLAN Trigonometric ratios test cover?
- Recognise the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles using properties of similarity.
- Questions may include word problems set in real Australian contexts
- Both calculator and non-calculator question types are covered
Try a sample Trigonometric ratios question
Question 1 — Easy
A ladder leans against a vertical wall. The foot of the ladder is 2.4 m from the base of the wall, and the ladder makes an angle of 68° with the ground. Priya wants to find the length of the ladder. Which expression correctly gives the ladder's length?
Answer: In the right-angled triangle, the 2.4 m distance is the side adjacent to the 68° angle and the ladder is the hypotenuse, so cos 68° = adjacent ÷ hypotenuse = 2.4 ÷ hypotenuse, giving hypotenuse = 2.4 ÷ cos 68°. Option B incorrectly multiplies instead of divides; option C confuses adjacent with opposite by using sine; option D calculates the height of the wall (opposite ÷ adjacent = tan), not the ladder's length.
Question 2 — Medium
A surveyor needs to find the height of a vertical cliff. Standing on flat ground, she measures the angle of elevation to the top of the cliff as 38°. She then walks 50 m directly towards the base of the cliff and measures the angle of elevation again as 62°. Determine the height of the cliff to the nearest metre.
Answer: Let the height of the cliff be h and the distance from the second observation point to the base be d. From the second position: tan 62° = h/d, so d = h/tan 62°. From the first position: tan 38° = h/(d + 50), so d + 50 = h/tan 38°. Subtracting: 50 = h/tan 38° − h/tan 62° = h(1/tan 38° − 1/tan 62°) ≈ h(1.2799 − 0.5317) = h × 0.7482, giving h ≈ 50/0.7482 ≈ 65 m. Option B (39 m) results from using tan 38° × 50 directly without setting up the two-equation system. Option C (88 m) arises from incorrectly adding the two tangent values rather than subtracting. Option D (53 m) comes from mistakenly using sin instead of tan in the ratio.
Question 3 — Hard
A rectangular sports field has a diagonal path running from one corner to the opposite corner. The path is 85 m long and makes an angle of 32° with the longer side of the field. Determine the length of the shorter side of the field, correct to one decimal place.
Answer: The shorter side is opposite the 32° angle, so sin(32°) = shorter side ÷ 85, giving 85 × sin(32°) ≈ 85 × 0.5299 ≈ 45.0 m. Option B uses cos(32°) instead of sin(32°), finding the longer side rather than the shorter side. Option C incorrectly uses tan(32°) × 85, treating the hypotenuse as an adjacent side. Option D applies the reciprocal operation (85 ÷ sin(32°)), confusing division with multiplication.
How should my child prepare for Year 9 NAPLAN Trigonometric ratios?
- Select Year 9 and Numeracy on the home screen
- Use Quick Practice — questions on trigonometric ratios will appear as part of the session
- Check the Skill Breakdown on your profile to track your accuracy on trigonometric ratios specifically
- Review explanations after each question to understand the reasoning behind correct answers
Skillo is free, requires no email or account details, and is built specifically for Australian students. Every question is mapped to the Australian Curriculum v9.0 and filtered by skill so your child practises exactly what they need.
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About this practice
Skillo's NAPLAN-style practice is authored independently. NAPLAN® is a registered trademark of ACARA. Skillo is not affiliated with, endorsed by, or sponsored by ACARA.