30°, 45°, 60°: Challenge & Extension
Mathematics
Year 9
17 questions
~34 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the exact sine, cosine, and tangent values for 30°, 45°, and 60°, including practice, reasoning, and extension questions.
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30°, 45°, 60°: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
1.
Recall the exact values of sine, cosine, and tangent for 30°, 45°, and 60°. Remember that these are derived from special triangles and are fundamental in trigonometry.
B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
Calculate sin 30°.
[1 mark]2.
Find cos 45°.
[1 mark]3.
Evaluate tan 60°.
[1 mark]4.
Express sin 45° as a simplified fraction.
[1 mark]C
Problem Solving & Reasoning
Show detailed working for each problem.
1.
A ladder leaning against a wall makes a 60° angle with the ground. If the ladder's length is 10 meters, find the height it reaches on the wall.
2.
A person walks 50 meters at an angle of 30° to the ground. How far is the person from their starting point in the straight line?
3.
Explain why sin 45° equals cos 45°, using geometric reasoning.
4.
A triangle has angles 30°, 60°, and 90°. Calculate the ratio of its side lengths opposite to these angles.
D
Real-world Applications
Apply your knowledge to contextual problems.
1.
An engineer needs to determine the length of a support beam inclined at 45°. If the vertical height of the building is 12 meters, what is the length of the beam?
E
Challenge & Extension
Attempt these advanced problems to deepen your understanding.
1.
Construct a right triangle with a 30° angle and hypotenuse of 15 cm. Calculate the length of the side opposite 30°, and verify it matches the known value.
2.
Derive the exact value of sin 75° using sum formulas involving 45° and 30°. Show all steps.
F
Mixed Review
Answer a variety of question types to reinforce your knowledge.
1.
Plot the graph of y = 2 sin x for x from 0° to 180° on the grid.
2.
Construct a triangle with sides 3, 4, and 5. Label the angles using exact trig values.
3.
Calculate tan 45° and verify the result equals 1.
G
Error Analysis
Identify and correct the mistakes in the following statements.
1.
A student claims that cos 60° = 1/2. They then conclude sin 60° = √3/2. Is this correct? Explain and correct the mistake if necessary.
2.
A person states that tan 30° = 1/√3. Is this accurate? Show the correct value and reasoning.
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet