MathsFreePrintable
Trigonometric Ratios Practice
A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
Trigonometric Ratios Practice
📐 Part 1: Understanding Trigonometric Ratios
1. In a right-angled triangle, which ratio represents sine θ?
adjacent ÷ hypotenuse
opposite ÷ hypotenuse
opposite ÷ adjacent
hypotenuse ÷ opposite
2. What does the tangent ratio equal?
sin θ ÷ cos θ
cos θ ÷ sin θ
opposite ÷ hypotenuse
adjacent ÷ hypotenuse
3. In a right-angled triangle with angle θ = 30°, hypotenuse = 10 cm, which calculation finds the opposite side?
10 × cos(30°)
10 × sin(30°)
10 × tan(30°)
10 ÷ sin(30°)
4. A ladder leans against a wall at 60° to the ground. The ladder is 8 metres long. How high up the wall does it reach?
8 × sin(60°) ≈ 6.9 metres
8 × cos(60°) = 4 metres
8 × tan(60°) ≈ 13.9 metres
8 ÷ sin(60°) ≈ 9.2 metres
🔢 Part 2: Calculations and Problem Solving
5. A tree casts a shadow 12 metres long when the angle of elevation to the sun is 35°. Calculate the height of the tree. Show your working.
Height = _________ metres (round to 1 decimal place)
6. From the top of a 25-metre tall building, the angle of depression to a car is 28°. How far is the car from the base of the building?
Distance = _________ metres (round to 1 decimal place)
7. In triangle ABC, angle C = 90°, side AB = 15 cm, and angle A = 42°. Find the length of side BC (opposite to angle A).
BC = _________ cm (round to 1 decimal place)
8. A wheelchair ramp has a horizontal distance of 6 metres and rises 0.5 metres vertically. What angle does the ramp make with the horizontal?
Angle = _________ degrees (round to 1 decimal place)
💭 Part 3: Reflection and Application
9. Explain in your own words when you would use the sine ratio instead of the cosine ratio.
10. Describe a real-world situation where you might need to use trigonometry. Explain which ratio you would use and why.
11. What challenges did you face when measuring angles and sides in today's practical activity? How did these affect your calculations?
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
More Maths Worksheets
Year 4
Year 4 Maths Placement Test
Free
Year 11
Functional Skills Maths Revision
Free
Year 11–13
Functional Skills Maths Assessment
Free
Year 11–13
Functional Skills Maths Practice
Free
Year 5–7
Maths Trivia Team Challenge
Free
Year 9
Year 9 Maths Revision
Free
Year 10
Year 10 Measurement Maths
Free
Year 8–9