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Turning Off Course

Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 37 of 44.

A walker or a ship that changes direction turns through some angle. The angle inside the triangle at the turning point is not that angle: it is 180° minus it, because the straight-on direction and the way back make a straight line.

$Walk 8 km to Q, turn 50° right, walk 5 km to R$

A hiker walks 8 km, turns 50° to the right and walks 5 km. The angle at the turn is 180° − 50° = 130°, so d^2 = 8^2 + 5^2 - 2×8×5×cos(130°) and she is about 11.85 km from the start. Using 50° by mistake would put her much closer.

Challenge

A hiker walks 12 km from P to Q, turns 70° to the right and walks 9 km to R. Find the distance x from P to R, to two decimal places, then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find x

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Triangles Without Right Angles

1Across the Lake

Across the Lake Sines Past 90°Cosines Past 90°Recap: Across the River

4Law of Cosines: SAS

The Law of Cosines An Obtuse Angle Between Through the Hill A Hooked Drive Recap: Two Sides, One Angle

7Area of a Triangle

Area With a Sine Area With an Obtuse Angle Working Backwards The Angle From the Area Heron's Formula Recap: A Garden Bed

2Law of Sines: AAS and ASA

Why the Law of Sines Holds Pair Side With Angle The Third Angle First Two Coast Stations Recap: Law of Sines

5Law of Cosines: SSS

Three Sides, One Angle The Largest Angle A Triangular Field Recap: Three Sides

8Bearings and Navigation

Reading Bearings Two Ships From PortTurning Off CourseFinding a Course Angle Recap: Ships at Sea

3The Ambiguous Case

Finding an Angle Two Triangles The Height Test An Obtuse Given Angle Radio Coverage Recap: How Many Triangles?

6Which Law to Use

Sines or Cosines?Not Between Three Towns Recap: Pick the Law

9Final Challenges

Final: Across the Canyon Final: Every Triangle Final: A Plot of Land Final: Ship and Plane Final: The Largest Angle