TOA: Real-world Applications in Gaming & Technology
Mathematics
GCSE Higher
12 questions
~24 mins
1 views0 downloads
About This Worksheet
A worksheet exploring the application of TOA in gaming and technology contexts. Students will practice calculating sides of right-angled triangles using trigonometry, with real-world scenarios relevant to modern technology.
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TOA: Real-world Applications in Gaming & Technology
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Read the following overview before attempting the questions.
1.
The TOA ratio relates the tangent of an angle to the ratio of the opposite side over the adjacent side in a right-angled triangle. Specifically, tan(θ) = opposite / adjacent. Use this relationship to find missing sides when given angles and one side length.
[2 marks]B
Fluency & Practice
Answer all questions. Show your working in the grid spaces provided.
1.
In a gaming setup, the camera is positioned 3 meters away from the screen at an angle of 30°. Calculate the height of the camera from the ground using TOA.
[3 marks]2.
A drone is flying at an angle of elevation of 45° from a point on the ground. If the drone is 50 meters away horizontally from the observer, find its vertical height.
[3 marks]3.
Calculate the length of the ladder leaning against a wall if the ladder makes an angle of 60° with the ground and the foot of the ladder is 4 meters from the wall.
[3 marks]C
Problem Solving & Reasoning
Answer carefully, showing detailed working.
1.
A gaming character is located 10 meters directly north of a tower. The angle of elevation from the character to the top of the tower is 35°. Find the height of the tower. Assume the ground between is level.
[4 marks]2.
A virtual reality headset tracks the position of a player at an angle of 45°. If the distance from the headset to the player’s hand is 2 meters, find the height difference between the head and hand using TOA.
[4 marks]D
Real-world Applications
Solve these contextual problems related to gaming and technology.
1.
A gaming drone hovers 20 meters away from a player at an angle of elevation of 40°. How high above the ground is the drone?
[3 marks]2.
In a virtual environment, a camera is positioned 5 meters from an object at an angle of 25°. Calculate the vertical height difference between the camera and the object.
[3 marks]E
Challenge & Extension
Attempt these advanced questions for extension.
1.
A new gaming setup involves a screen tilted at an angle of 50°. If the distance from the player to the screen's base is 3 meters, find the height of the top of the screen above the player's eye level.
[4 marks]2.
A virtual reality system requires the user’s eye level to be 1.2 meters above the ground. If the headset is positioned 2 meters away at an angle of 60°, what is the height of the headset relative to the user’s eye level?
[4 marks]F
Mixed Review & Error Analysis
Answer the following questions and identify common mistakes.
1.
A player’s device is positioned 8 meters away from a virtual object at an angle of 55°. Calculate the height difference between the device and the object. (Incorrect answer: 6.4 meters, correct approach?)
[2 marks]2.
Identify the mistake: A student calculates tan(45°) as 1.5 instead of 1. Why is this incorrect? Fix the calculation for an angle of 45° with an opposite side of 3 meters and find the adjacent side.
[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