Solving Triangles in Surveying

Key idea

Triangulation to measure inaccessible distances.

In depth

Surveyors measure baselines and angles, then use sine and cosine rules to compute inaccessible distances through triangulation. Accuracy depends on keeping triangles well-shaped, not too thin.

Worked example

From a baseline of 100 m, angles of 50° and 70° to a tree give distance via the law of sines: 100 sin 70°/sin 60° ≈ 108.5 m.

Real-world uses

• Measuring the width of a river or the distance to an inaccessible island using triangulation

Common mistake

Using a bad triangle with a tiny angle, which magnifies errors.

How to learn this

1. Read the key idea and say it in your own words.
2. Work through the worked example, then try a similar problem.
3. Use the interactive lesson’s visual and mini-quiz to check the pattern.

Frequently asked questions

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Related advanced topics in Trigonometry

• Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
• Phase Shift – Horizontal translation of a wave.
• Vertical Shift and Midline – Moves the wave up or down.
• General Sinusoid – Combine amplitude, period, phase and shift.
• Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
• Pythagorean Identity – The key identity from the unit circle.