TOA: Mixed Review
Mathematics
Year 9
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet providing a mixed review on using TOA in trigonometry to find sides of right-angled triangles, including procedural, application, and extension problems.
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TOA: Mixed Review
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Introduction
Review the fundamental formula: tan(θ) = opposite / adjacent. Use this to find missing sides in right-angled triangles using TOA.
B
Fluency & Practice
Answer the following questions to practice using TOA to find sides.
1.
In a right-angled triangle, the angle θ is 30°, and the length of the adjacent side is 8 cm. Calculate the length of the opposite side.
[3 marks]2.
A ladder leans against a wall forming a 45° angle with the ground. The length of the ladder is 10 meters. Find the length of the side opposite to the angle (height up the wall).
[3 marks]3.
Calculate the value of tan(60°).
[2 marks]4.
A right triangle has an opposite side of 5 cm and an angle of 45°. Find the length of the adjacent side.
[3 marks]C
Problem Solving & Reasoning
Apply your understanding of TOA in multi-step problems.
1.
A ramp makes an angle of 30° with the ground. If the vertical height of the ramp is 3 meters, find the length of the ramp.
[4 marks]2.
A tree casts a shadow of 12 meters when the sun is at an angle of elevation of 40°. Calculate the height of the tree.
[4 marks]3.
In a right triangle, the opposite side is 9 cm and the angle is 60°. Find the length of the hypotenuse.
[3 marks]D
Real-world Applications
Solve these word problems based on real-world contexts.
1.
A cyclist is riding up a hill. The angle of elevation is 20°, and the horizontal distance traveled is 150 meters. Find the vertical height gained.
[4 marks]2.
A lighthouse stands 50 meters tall. The angle of depression to a boat on the sea is 10°. How far is the boat from the lighthouse?
[4 marks]E
Challenge & Extension
Tackle these advanced problems to extend your understanding.
1.
Construct a right triangle where the opposite side is twice the length of the adjacent side, and the angle θ is 45°. Find the lengths of all sides.
[4 marks]2.
A satellite is in orbit making a 60° angle with the ground. If its altitude is 500 km, find the distance from the satellite to the point directly beneath it on the ground.
[4 marks]F
Mixed Review & Error Analysis
Answer these questions to review your understanding and identify common mistakes.
1.
A student calculates tan(45°) as 1, which is correct. However, they then find the opposite side as 7 cm and the adjacent as 7 cm to get the hypotenuse. Identify and correct the mistake.
[4 marks]2.
If a student uses sine instead of tangent for a side calculation, what common mistake might they make? Explain briefly.
[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.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet