Free Printable Worksheets

Choose a Right-Triangle Ratio: Club Practice

In a right triangle, relative to angle θ, the opposite leg is 8, adjacent leg is 15, and hypotenuse is 17. Sine = opposite/hypotenuse; cosine = adjacent/hypotenuse; tangent = opposite/adjacent.

Use the supplied scenario and model. Show calculations or explain the evidence requested in each task.

1.Find sin θ as a fraction.

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Grade 10

Key

Choose a Right-Triangle Ratio: Club Practice

Practice · Independent · 30 min

Choose a Right-Triangle Ratio: Club Practice. Grade 10 printable practice: Choose and interpret trigonometric ratios using a stated reference angle. Includes five tasks, matching answers, and teacher guidance. Print on US Letter or A4, or save as PDF from the print window.

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Choose a Right-Triangle Ratio: Garden Practice

In a right triangle, relative to angle θ, the opposite leg is 3, adjacent leg is 4, and hypotenuse is 5. Sine = opposite/hypotenuse; cosine = adjacent/hypotenuse; tangent = opposite/adjacent.

Use the supplied scenario and model. Show calculations or explain the evidence requested in each task.

1.Find sin θ as a fraction.

Practice preview

Grade 10

Key

Choose a Right-Triangle Ratio: Garden Practice

Practice · Independent · 30 min

Choose a Right-Triangle Ratio: Garden Practice. Grade 10 printable practice: Choose and interpret trigonometric ratios using a stated reference angle. Includes five tasks, matching answers, and teacher guidance. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Choose a Right-Triangle Ratio: Library Practice

In a right triangle, relative to angle θ, the opposite leg is 5, adjacent leg is 12, and hypotenuse is 13. Sine = opposite/hypotenuse; cosine = adjacent/hypotenuse; tangent = opposite/adjacent.

Use the supplied scenario and model. Show calculations or explain the evidence requested in each task.

1.Find sin θ as a fraction.

Practice preview

Grade 10

Key

Choose a Right-Triangle Ratio: Library Practice

Practice · Independent · 30 min

Choose a Right-Triangle Ratio: Library Practice. Grade 10 printable practice: Choose and interpret trigonometric ratios using a stated reference angle. Includes five tasks, matching answers, and teacher guidance. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Choose a Right-Triangle Ratio: Workshop Practice

In a right triangle, relative to angle θ, the opposite leg is 7, adjacent leg is 24, and hypotenuse is 25. Sine = opposite/hypotenuse; cosine = adjacent/hypotenuse; tangent = opposite/adjacent.

Use the supplied scenario and model. Show calculations or explain the evidence requested in each task.

1.Find sin θ as a fraction.

Practice preview

Grade 10

Key

Choose a Right-Triangle Ratio: Workshop Practice

Practice · Independent · 30 min

Choose a Right-Triangle Ratio: Workshop Practice. Grade 10 printable practice: Choose and interpret trigonometric ratios using a stated reference angle. Includes five tasks, matching answers, and teacher guidance. Print on US Letter or A4, or save as PDF from the print window.

Printable activity

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Coordinate Transformations and Proof

Translate a coordinate triangle

A(0,0), B(3,0), C(0,4) and D(6,2), E(9,2), F(6,6) define two triangles. Correspondence is A↔D, B↔E, C↔F. Give reasons from coordinates or rigid motions; a similar-looking sketch alone is not a proof.

Worked example: Translation (2, −1) takes P(1,3) to P′(3,2). It preserves lengths; a dilation of factor 3 usually changes lengths. Use the material to work through each task. Show the requested response.

1.Write the translation vector taking A to D.

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Grade 10

Key

Coordinate Transformations and Proof

Practice · Independent · 45 min

Map corresponding vertices with a rigid motion. Calculate and compare side lengths. Build a congruence argument and distinguish a dilation. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Right Triangle Ratios and Similarity

A reference angle in a right triangle

The right angle is at the lower left. Angle A is the lower-right acute angle. The opposite leg is 3, adjacent leg 4, and hypotenuse 5. All lengths use the same unit. Ratios depend on the chosen angle; the sketch is not to scale.

Worked example: For opposite 6, adjacent 8 and hypotenuse 10, sin A = 6/10 = 3/5. A similar triangle with hypotenuse 20 has opposite leg 12. Use the material to work through each task. Show the requested response.

1.Name the opposite leg and hypotenuse relative to A.

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Grade 10

Key

Right Triangle Ratios and Similarity

Practice · Independent · 45 min

Identify sides relative to an acute reference angle. Calculate ratios and corresponding lengths. Justify complementary-angle relationships and apply a ratio. A complete set with exploration, practice and application. Use the linked unit for the learning sequence and teaching guide.

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Coordinate Transformations and Proof: Apply and Create

Translate a coordinate triangle

A(0,0), B(3,0), C(0,4) and D(6,2), E(9,2), F(6,6) define two triangles. Correspondence is A↔D, B↔E, C↔F. Give reasons from coordinates or rigid motions; a similar-looking sketch alone is not a proof.

Use what you learned to explain, construct or apply an idea.

1.Prove triangle ABC is congruent to triangle DEF using a rigid motion or SSS. State the correspondence.

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Grade 10

Key

Coordinate Transformations and Proof: Apply and Create

Apply · Independent · 25 min

Map corresponding vertices with a rigid motion. Calculate and compare side lengths. Build a congruence argument and distinguish a dilation. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

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Coordinate Transformations and Proof: Explore and Explain

Translate a coordinate triangle

A(0,0), B(3,0), C(0,4) and D(6,2), E(9,2), F(6,6) define two triangles. Correspondence is A↔D, B↔E, C↔F. Give reasons from coordinates or rigid motions; a similar-looking sketch alone is not a proof.

Worked example: Translation (2, −1) takes P(1,3) to P′(3,2). It preserves lengths; a dilation of factor 3 usually changes lengths. Explore the material. Talk through your reasoning with suitable support.

1.Write the translation vector taking A to D.

Practice preview

Grade 10

Key

Coordinate Transformations and Proof: Explore and Explain

Explore · Independent · 12 min

Map corresponding vertices with a rigid motion. Calculate and compare side lengths. Build a congruence argument and distinguish a dilation. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

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Practice preview

Grade 10

Key

Coordinate Transformations and Proof: Practice Independently

Practice · Independent · 20 min

Map corresponding vertices with a rigid motion. Calculate and compare side lengths. Build a congruence argument and distinguish a dilation. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Right Triangle Ratios and Similarity: Apply and Create

A reference angle in a right triangle

The right angle is at the lower left. Angle A is the lower-right acute angle. The opposite leg is 3, adjacent leg 4, and hypotenuse 5. All lengths use the same unit. Ratios depend on the chosen angle; the sketch is not to scale.

Use what you learned to explain, construct or apply an idea.

1.For the other acute angle B, write sin B and explain why it equals cos A.

Practice preview

Grade 10

Key

Right Triangle Ratios and Similarity: Apply and Create

Apply · Independent · 25 min

Identify sides relative to an acute reference angle. Calculate ratios and corresponding lengths. Justify complementary-angle relationships and apply a ratio. A focused apply activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Right Triangle Ratios and Similarity: Explore and Explain

A reference angle in a right triangle

The right angle is at the lower left. Angle A is the lower-right acute angle. The opposite leg is 3, adjacent leg 4, and hypotenuse 5. All lengths use the same unit. Ratios depend on the chosen angle; the sketch is not to scale.

Worked example: For opposite 6, adjacent 8 and hypotenuse 10, sin A = 6/10 = 3/5. A similar triangle with hypotenuse 20 has opposite leg 12. Explore the material. Talk through your reasoning with suitable support.

1.Name the opposite leg and hypotenuse relative to A.

Practice preview

Grade 10

Key

Right Triangle Ratios and Similarity: Explore and Explain

Explore · Independent · 12 min

Identify sides relative to an acute reference angle. Calculate ratios and corresponding lengths. Justify complementary-angle relationships and apply a ratio. A focused learn activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Right Triangle Ratios and Similarity: Practice Independently

A reference angle in a right triangle

The right angle is at the lower left. Angle A is the lower-right acute angle. The opposite leg is 3, adjacent leg 4, and hypotenuse 5. All lengths use the same unit. Ratios depend on the chosen angle; the sketch is not to scale.

Use the material to work through each task. Show the requested response.

1.Find cos A in simplest form.

Practice preview

Grade 10

Key

Right Triangle Ratios and Similarity: Practice Independently

Practice · Independent · 20 min

Identify sides relative to an acute reference angle. Calculate ratios and corresponding lengths. Justify complementary-angle relationships and apply a ratio. A focused practice activity. Use the linked unit for the learning sequence and teaching guide.

Choose another practice set

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Geometry & Trigonometry: SOH CAH TOA & Right Triangles

Part A: Trigonometric Calculations. Apply SOH CAH TOA to determine exact ratios and side lengths.

1.In right triangle ABC with right angle at C, leg AC (adjacent to angle A) = 15 cm and hypotenuse AB = 17 cm. What is the value of cos(A)?

2.A surveyor stands 100 meters away from the base of a telecommunications tower on level ground. The angle of elevation from the ground to the top of the tower is 30°. Given that tan(30°) ≈ 0.577, what is the approximate height of the tower?

Grade 10

HSG.SRT.C.6 Key