3D Trigonometry Applications
3D trigonometry extends sine, cosine, and tangent rules to solve problems involving angles of elevation, depression, and bearings in three-dimensional space.
What You Need to Know
Key Concept Diagram
Angle of elevation is measured upward from the horizontal to a line of sight
Angle of depression is measured downward from the horizontal to a line of sight
The sine rule: a/sin A = b/sin B = c/sin C relates sides and angles in any triangle
The cosine rule: c^2 = a^2 + b^2 - 2ab cos C is used when two sides and the included angle are known
3D problems are solved by identifying and solving 2D triangles within the 3D shape
Key Vocabulary
Angle of elevation
The angle measured upward from the horizontal to an object above
Angle of depression
The angle measured downward from the horizontal to an object below
Sine rule
A relationship between the sides and angles of any triangle
Bearing
A direction measured as a clockwise angle from north
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A person stands 50 m from the base of a tower. The angle of elevation to the top is 30 degrees. How tall is the tower?
Question 2
In triangle ABC, a = 8, b = 6, and angle C = 90 degrees. Find c.
Question 3
The sine rule states:
Key Concepts Summary
- ●Angle of elevation is measured upward from the horizontal to a line of sight
- ●Angle of depression is measured downward from the horizontal to a line of sight
- ●The sine rule: a/sin A = b/sin B = c/sin C relates sides and angles in any triangle
- ●The cosine rule: c^2 = a^2 + b^2 - 2ab cos C is used when two sides and the included angle are known
- ●3D problems are solved by identifying and solving 2D triangles within the 3D shape