CAH: Real-world Applications
Mathematics
Grade 6
11 questions
~22 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on the CAH component of SOHCAHTOA, applying it to real-world and mathematical problems. Designed for Grade 6 students to develop procedural mastery and problem-solving skills.
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Full preview • 11 questions
CAH: Real-world Applications
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Practice Questions
Answer all questions. Show your working in the grid spaces provided.
1.
In a right-angled triangle, the angle is 30° and the side adjacent to the angle is 5 meters. Use CAH to find the length of the hypotenuse.
[3 marks]2.
A ladder leans against a wall, forming a 45° angle with the ground. The distance from the base of the ladder to the wall is 4 meters. Calculate the length of the ladder using CAH.
[3 marks]3.
Explain how to find the hypotenuse in a right triangle if you are given the measure of the adjacent side and the angle, using CAH.
[2 marks]4.
A car's navigation system shows that the angle of elevation to a hilltop is 20°. If the distance from the car to the hill is 1,000 meters along the ground, find the height of the hill using CAH.
[3 marks]5.
A crane lifts a load, and the angle between the ground and the cable is 60°. If the length of the cable is 20 meters, find the height at which the load is lifted.
[3 marks]6.
A person is standing 10 meters away from a monument. The angle of elevation to the top of the monument is 35°. Use CAH to find the height of the monument.
[3 marks]7.
A surveyor measures the angle of a slope as 25°. The adjacent distance along the ground is 80 meters. Calculate the slope's length using CAH.
[3 marks]8.
A lighthouse keeper checks that the angle of depression to a boat is 15°. If the boat is 2 km away horizontally, estimate the height of the lighthouse using CAH.
[3 marks]9.
A drone flies at a height of 50 meters and forms a 40° angle with a point directly below it. Compute the distance from the drone to that point using CAH.
[3 marks]10.
Identify and correct the mistake in this solution: 'Given a 60° angle and an adjacent side of 8 meters, the hypotenuse is 8 / cos(60°) = 8 / 0.5 = 16 meters.'
[2 marks]11.
Challenge: A satellite observes a building at a 70° angle of elevation from a point 150 meters away horizontally. Use CAH to find the height of the building. Show all working.
[4 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)
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet