Key Stage 4 Mathematics - Introduction to Trigonometry

Duration: 1 hour

Objectives:

• To understand the basic concepts of trigonometry
• To use the sine, cosine, and tangent ratios in right-angled triangles
• To solve simple problems using trigonometry

Materials:

• Whiteboard and markers
• Protractor and ruler
• Handout with practice problems

Introduction (10 minutes):

• Ask students if they have heard of trigonometry and what they know about it
• Introduce trigonometry as the study of the relationships between the sides and angles of triangles
• Explain the three main trigonometric ratios: sine, cosine, and tangent

Body (35 minutes):

• Provide examples of right-angled triangles and demonstrate how to use the sine, cosine, and tangent ratios to find unknown sides and angles
• Provide practice problems for students to solve in pairs or independently
• Discuss the relationships between the ratios (e.g. reciprocal, Pythagorean)
• Demonstrate how to use a protractor and ruler to measure angles in degrees

Conclusion (15 minutes):

• Review the key concepts covered in the lesson
• Answer any questions students may have
• Assign homework (e.g. additional practice problems or a worksheet)
• Summarize what will be covered in the next lesson

Assessment:

• Observe students during the practice problems to assess understanding
• Collect and grade the homework to see how well students have retained the material

Note: This is just a sample lesson plan, and can be adjusted to fit the needs of your students and curriculum. 

Handout: 

Introduction to Trigonometry Practice Problems

Instructions:

• Solve each problem using the concepts covered in the lesson on Introduction to Trigonometry
• Show your work for each problem
• Discuss your strategies and solutions with your partner

Problem 1:

In a right triangle with sides a = 6 units and b = 8 units, find the length of the hypotenuse c.

Problem 2: 

In a right triangle with sides a = 8 units and b = 10 units, find the value of sin A, cos A, and tan A where A is one of the acute angles in the triangle.

Problem 3: 

In a right triangle with hypotenuse c = 12 units and one acute angle A = 30 degrees, find the length of sides a and b.

Problem 4: 

A ladder leans against a wall and reaches a height of 20 feet. If the ladder is 18 feet long, what is the angle between the ground and the ladder?

Problem 5: 

A building is 50 feet tall and a flagpole is 20 feet away from the building. How high does the flagpole reach on the building?

Problem 6: 

An airplane takes off from an airport with a runway that is 10,000 feet long. The runway makes an angle of 10 degrees with the horizontal. How high is the airplane after it takes off?

Note: These are just sample problems, and can be adjusted to fit the needs of your students and curriculum. The purpose of these problems is to provide opportunities for students to apply the trigonometry concepts they have learned.