30°, 45°, 60°: Error Analysis & Misconceptions
Mathematics
Grade 8
15 questions
~30 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on identifying and correcting common misconceptions related to exact sine, cosine, and tangent values of 30°, 45°, and 60°. Designed to promote deeper understanding through error analysis and application.
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30°, 45°, 60°: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 8
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Untitled Worksheet
Grade Grade 8
A
Fluency & Practice
Calculate the following exact trig values and identify any common mistakes in your working.
1.
Calculate sin 30° and explain your reasoning.
[2 marks]2.
Calculate cos 45° and provide your working steps.
[2 marks]3.
Find tan 60°, showing all steps.
[2 marks]4.
Identify the common mistake in calculating sin 45° as 1/√2 and correct it.
[3 marks]B
Error Analysis & Misconceptions
Review the following incorrect calculations. Identify the mistake and correct it.
1.
A student claims that cos 30° = 1/2. Is this correct? If not, what is the correct value?
[1 mark]ACorrect
BIncorrect; correct value is 1/2
CIncorrect; correct value is √3/2
DIncorrect; correct value is 1/√2
2.
A calculation shows tan 45° = 1.1. What mistake might lead to this error?
[2 marks]C
Problem Solving & Reasoning
Solve these multi-step problems involving 30°, 45°, 60° trig values. Show all your reasoning.
1.
A ladder leans against a wall forming a 60° angle with the ground. If the ladder's length is 10 meters, find the height it reaches on the wall.
[4 marks]2.
A flagpole casts a shadow of length 8 meters when the sun is at an angle of 45°. Find the height of the flagpole.
[4 marks]3.
In a right triangle with an angle of 30°, if the hypotenuse is 12, find the length of the side opposite 30°.
[2 marks]D
Real-world Applications
Apply your understanding of exact trig values to solve these real-world problems.
1.
A boat is sailing at a 45° angle to the shoreline. If it travels 20 km along that path, how far is it from the shoreline?
[3 marks]2.
A ramp rises at an angle of 30° and is 15 meters long. Find the vertical height of the ramp.
[3 marks]E
Challenge & Extension
Tackle these advanced problems involving multiple steps and misconceptions.
1.
A triangle has angles of 30°, 60°, and 90°. The side opposite 30° is 5 cm. Find the lengths of the other two sides.
[4 marks]2.
Explain why sin 45° is equal to cos 45°, and demonstrate with an example.
[3 marks]F
Mixed Review
Answer the following variety of questions to reinforce your understanding.
1.
Construct a right triangle with a 45° angle and hypotenuse of length 10. Draw and label the triangle.
[3 marks]2.
Plot the graph of y=2x for x from 0 to 5 on the grid.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet