Grade 10 Trigonometry Worksheets
Free printable trigonometry practice for Grade 10 students. Generate problems, solve them on screen or paper, and download as PDF.
Practice Worksheet
Grade 10 Trigonometry Practice
Solve each problem. Show your work.
- 1.A right triangle has opposite side 8 cm and adjacent side 9 cm. Find θ to the nearest degree: _____
- 2.A right triangle has hypotenuse 10 cm and angle 30°. Find the opposite side to 1 decimal place: _____
- 3.From 20 m away, the angle of elevation to a building is 45°. Find the building height: _____
- 4.A right triangle has opposite side 4 cm and adjacent side 10 cm. Find θ to the nearest degree: _____
- 5.A right triangle has hypotenuse 12 cm and angle 30°. Find the opposite side to 1 decimal place: _____
- 6.From 25 m away, the angle of elevation to a building is 45°. Find the building height: _____
Show answer key
- Question 1: 42°
- Question 2: 5.0 cm
- Question 3: 20 m
- Question 4: 22°
- Question 5: 6.0 cm
- Question 6: 25 m
Free Practice Worksheets
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Build confidence with approachable problems
Solve each problem. Round your answers to two decimal places where necessary.
- 1.In a right triangle, angle A = 30 degrees and the side opposite to angle A is 5. Find the length of the hypotenuse using the sine ratio.
- 2.In a right triangle with legs of length 6 and 8, find the measure of the angle opposite to the side of length 6 using the tangent ratio.
- 3.Triangle ABC has side a = 10, side b = 12, and angle C = 40 degrees. Use the cosine law to find the length of side c.
- 4.In triangle ABC, angle A = 50 degrees, side a = 15, and angle B = 60 degrees. Use the sine law to find the length of side b.
- 5.Triangle ABC is similar to Triangle DEF. In ABC, sides are 3, 4, and 5. If the side corresponding to 3 in Triangle DEF is 9, find the length of the side corresponding to 4.
- 6.In a right triangle, the hypotenuse is 10 and one angle is 45 degrees. Find the length of the side adjacent to the 45-degree angle.
A selection of topic skills
Solve each problem. Show your work.
- 1.In a right-angled triangle, the hypotenuse is 15 cm and one angle is 35 degrees. Calculate the length of the side adjacent to the 35-degree angle. Round your answer to the nearest tenth.
- 2.Triangle ABC is similar to Triangle DEF. If AB = 4 cm, BC = 6 cm, and DE = 10 cm, find the length of EF.
- 3.In triangle XYZ, angle X = 50 degrees, side x = 12 cm, and side y = 10 cm. Use the Sine Law to find the measure of angle Y. Round your answer to the nearest degree.
- 4.In triangle PQR, side p = 7 cm, side q = 9 cm, and angle R = 60 degrees. Use the Cosine Law to find the length of side r. Round to the nearest tenth.
- 5.A ladder 8 meters long leans against a wall. The base of the ladder is 3 meters away from the base of the wall. What angle does the ladder make with the ground? Round your answer to the nearest degree.
- 6.Two hikers are 5 km apart. They both spot a mountain peak. Hiker A measures an angle of elevation of 40 degrees, and Hiker B measures an angle of elevation of 35 degrees. If the hikers are on opposite sides of the mountain, how far is the peak from Hiker A? Use the Sine Law.
Practise specific Trigonometry skills
Skill map
How trigonometry skills connect
Shore up what feeds in, work through the core skills in order, then move on to what they unlock. A means the skill has an instant answer checker.
What Your Child Will Learn
Grade 10 trigonometry begins with similar triangles — establishing that equal angles produce proportional sides — before moving into right-triangle trigonometry using SOH-CAH-TOA to find missing sides and angles. Students practise setting up the correct ratio (sine, cosine, or tangent) based on which sides and angles are known, then solve for unknowns using inverse trig functions on a calculator.
The unit then extends beyond right triangles: the sine law and cosine law let students solve for sides and angles in acute and, in some courses, oblique triangles where no right angle exists. Students learn to recognize which law applies based on the given information (an angle-side-side situation calls for sine law, a side-angle-side situation calls for cosine law) and handle the ambiguous case where sine law can yield zero, one, or two valid triangles.
Applications are heavily contextual — height and distance problems involving angles of elevation and depression, navigation and bearing problems, and indirect measurement scenarios where a direct measurement isn't possible. These problems demand careful diagram-drawing, which is often the single biggest factor in getting a trig word problem right.
Skills Covered
- Solving right triangles using SOH-CAH-TOA
- Applying angles of elevation and depression
- Using the sine law to solve for unknown sides and angles
- Using the cosine law to solve for unknown sides and angles
- Recognizing which trig law applies given the known information
- Drawing accurate diagrams to model trigonometric word problems
Curriculum Aligned: Core strand of Grade 10 math (MPM2D and MFM2P), covering right-triangle trigonometry through to the sine and cosine laws for non-right triangles.
Parent Tip: A calculator set to the wrong angle mode (degrees vs. radians) is one of the most common — and most invisible — errors at this level. If an answer looks wildly off, that's the first thing worth checking together before assuming the setup itself was wrong.
What your child will practice
- Similar TrianglesVerify properties of similar triangles and solve problems using similarity.
- Primary Trigonometric RatiosDetermine the values of sine, cosine, and tangent ratios for acute angles in right triangles.
- Sine LawApply the sine law to solve problems involving acute triangles.
- Cosine LawApply the cosine law to solve problems involving acute triangles.
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Check my workFrequently Asked Questions
How often should my child practice trigonometry?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.