Angles of Elevation/Depression in 3D: Problem Solving & Reasoning

Mathematics
GCSE Higher
10 questions
~20 mins
1 views0 downloads

About This Worksheet

A worksheet covering angles of elevation and depression in 3D space, focusing on problem solving and reasoning skills required for GCSE Higher students.

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Angles of Elevation/Depression in 3D: Problem Solving & Reasoning

Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet

Grade GCSE Higher
A

Introduction

Read the key concepts carefully before attempting the questions. Recall that the angle of elevation/depression is the angle between the horizontal and the line of sight from the observer to the object, often involving right-angled triangles in 3D.
B

Practice Questions

Answer all questions. Show your working in the grid spaces provided.
1.
Calculate the angle of elevation from the top of a building 50 meters high to the top of a flagpole 150 meters away horizontally.
[2 marks]
2.
A person observes a ship at an angle of depression of 10° from the top of a lighthouse 80 meters high. Calculate the horizontal distance from the lighthouse to the ship.
[3 marks]
3.
Construct a right-angled triangle on the grid representing a building 60 meters high with a line of sight inclined at 30°. Use the grid to find the distance from the observer to the base of the building.
[3 marks]
4.
A drone is flying at an altitude of 120 meters. Its camera is directed at an angle of 45° of depression towards a point on the ground. Calculate the horizontal distance from the drone to that point.
[2 marks]
5.
A plane at an altitude of 10,000 meters observes a mountain at an angle of elevation of 20°. Calculate the horizontal distance from the plane to the mountain.
[3 marks]
6.
In a 3D scenario, the observer is 40 meters above ground level on a hill, looking at a car 100 meters away horizontally at an angle of depression of 15°. Find the height of the car from the ground level.
[3 marks]
7.
A satellite orbits 300 km above the Earth's surface. It observes a point on the ground at an angle of elevation of 60°. Calculate the horizontal distance from the satellite to that point.
[3 marks]
8.
A hiker on a mountain views a lake at an angle of depression of 25°. The height of the mountain is 500 meters. Calculate the horizontal distance to the lake.
[3 marks]
9.
A lighthouse is 70 meters tall. A boat at sea observes the top of the lighthouse at an angle of elevation of 15°. Calculate the distance from the boat to the lighthouse.
[2 marks]
10.
Identify and correct the mistake in the following reasoning: 'Since the angle of elevation to a mountain is 30°, and the height of the mountain is 900 meters, the horizontal distance must be 900 × tan 30° = 519.62 meters.'
[4 marks]

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Details

Created
1/1/2026
Updated
1/1/2026
Type
worksheet