Triangulation Calculator
Determine unknown coordinates using triangulation methods for surveying and navigation
Triangulation Calculation
x-coordinate
y-coordinate
x-coordinate
y-coordinate
Bearing to unknown landmark
Bearing to unknown landmark
Landmark Location
Calculation Steps:
tan(α) = tan(30°) = 0.5774
tan(β) = tan(330°) = -0.5774
x₃ = (y₁ - y₂ + x₂×tan(β) - x₁×tan(α)) / (tan(β) - tan(α))
y₃ = (y₁×tan(β) - y₂×tan(α) + (x₂ - x₁)×tan(β)×tan(α)) / (tan(β) - tan(α))
Triangulation Quality
Example Calculation
Land Surveying Example
Observation Point A: (0, 0)
Observation Point B: (5, 0)
Bearing from A: 30° (to unknown landmark)
Bearing from B: 330° (to unknown landmark)
Solution
tan(30°) = 0.5774, tan(330°) = -0.5774
x₃ = (0 - 0 + 5×(-0.5774) - 0×0.5774) / (-0.5774 - 0.5774)
x₃ = -2.887 / -1.1548 = 2.5
y₃ = (0×(-0.5774) - 0×0.5774 + (5 - 0)×(-0.5774)×0.5774) / (-0.5774 - 0.5774)
Landmark Location: (2.5, 4.33)
Triangulation Methods
Intersection
Find unknown landmark location
Observe from two known points
Resection
Determine your own position
Observe two known landmarks
Surveying Tips
Optimal intersection angles: 30° to 150°
Avoid narrow angles for better accuracy
Use precise bearing measurements
Verify results with additional observations
Understanding Triangulation
What is Triangulation?
Triangulation is a surveying and navigation method that determines the location of an unknown point by measuring angles from known positions. It forms triangles to calculate precise coordinates using trigonometric principles.
Applications
- •Land surveying and mapping
- •Navigation and positioning
- •Civil engineering projects
- •Astronomical observations
Mathematical Formula
x₃ = (y₁ - y₂ + x₂×tan(β) - x₁×tan(α)) / (tan(β) - tan(α))
y₃ = (y₁×tan(β) - y₂×tan(α) + (x₂ - x₁)×tan(β)×tan(α)) / (tan(β) - tan(α))
- (x₃, y₃): Unknown point coordinates
- (x₁, y₁), (x₂, y₂): Known point coordinates
- α, β: Bearing angles in degrees
- tan(α), tan(β): Tangent of bearing angles
Note: Lines must not be parallel (different slopes) for a unique solution.
Triangulation vs. Trilateration
Triangulation
- •Uses angle measurements
- •Requires line-of-sight visibility
- •Historical surveying method
- •Precise angular measurements needed
Trilateration
- •Uses distance measurements
- •No line-of-sight required
- •Modern GPS technology
- •Time/radio signal measurements