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G-SRT.11 Core M3-043-R06-V03

Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.

Convert bearings into a solvable triangle

Problem

A route travels \(15~\text{km}\) on bearing \(020°\), then \(22~\text{km}\) on bearing \(100°\), as shown. Find the reverse bearing of the first leg at the turn, determine the included angle, and calculate the displacement.

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At the turn, the reverse first-leg bearing is 200°, so the included angle is 100°. d²=15²+22²-2·15·22cos(100°), giving d≈28.7 km.

Ignore the bearing change and add the legs, d=15+22=37 km.

Force a sine pair d/sin(100°)=22/sin(15°), giving d≈83.7 km.

Use the forward-bearing difference 100°-20°=80°: d²=15²+22²-2·15·22cos(80°), giving d≈24.4 km.

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Curriculum context

Course: Math III
Standard: G-SRT.11
Category: Geometry
Domain: Similarity, Right Triangles, and Trigonometry
Objective: Apply the Laws of Sines and Cosines to find unknown measurements in right and non-right triangles.
Problem type: Convert bearings into a solvable triangle