90°: Real-world Applications in Travel & Maps
Mathematics
Year 9
10 questions
~20 mins
1 views0 downloads
About This Worksheet
This worksheet explores the key concept that angles in a semicircle are always 90°, applying it to travel and map scenarios. Students will develop procedural skills and reasoning in real-world contexts.
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90°: Real-world Applications in Travel & Maps
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
On a map, a diameter of a circular lake is 6 km long. What is the measure of the angle between two straight paths from a point on the circle passing through the endpoints of the diameter?
[2 marks]2.
Calculate the angle at a point on a circular roundabout if the two roads intersect at the ends of a diameter of the circle.
[2 marks]3.
A cyclist travels along a circular park with a diameter of 400 meters. If the cyclist starts at a point on the circumference and travels to a point directly opposite, what is the angle formed with the diameter?
[2 marks]4.
Construct a diagram showing a semicircular map route where an angle inscribed in the semicircle is 90°. Label the key points.
[3 marks]5.
In a city map, a bridge connects two points on the edge of a circular river. If the bridge forms a 90° angle with the diameter passing through these points, what is the length of the bridge if the radius of the river is 5 km?
[3 marks]6.
A road runs from a point on a circular roundabout to a point on the circumference, passing through the center. If the radius of the roundabout is 300 meters, what is the measure of the angle at the point on the circumference?
[2 marks]7.
A traveler plans to walk from a point on a circular city park’s boundary to a point directly across the park, passing through the center. If the radius of the park is 150 meters, what is the angle at the boundary point?
[2 marks]8.
Identify and correct the mistake in the following statement: 'Angles inscribed in a semicircle are always 180°.'
[2 marks]9.
A map shows a circular island with a diameter of 10 km. A boat travels from one point on the circumference to another point passing through the center of the island. What is the angle between the boat's route and a tangent to the circle at the starting point?
[3 marks]10.
A circular viewing platform has a radius of 20 meters. An engineer plans a walkway from a point on the edge to another point directly opposite, passing through the center. Calculate the angle at the starting point where the walkway meets the edge.
[2 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet