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A Triangular Field

Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 23 of 44.

A farmer has a three-sided field and wants the angle at one corner, to set a fence post. Pacing out the three sides is easy; measuring the angle is not.

$A field with sides 80 m, 100 m and 130 m and the corner angle φ at P$

Sides 80, 100 and 130 m, and the angle φ at P between the 100 m and 130 m sides, across from 80 m: 80^2 = 100^2 + 130^2 - 2×100×130×cos(phi), so cos φ = 20500/26000 and φ is about 37.96°.

This is the smallest angle of the field, since 80 m is the shortest side. A good check: the angles at the other corners must be larger.

Challenge

A triangular field has sides of 120 m, 150 m and 200 m. Find the angle θ across from the 120 m side, to two decimal places, and press Check.

Try it yourself

$Use the figure to find theta$

Use the figure to find theta

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 AngleA Triangular FieldRecap: Three Sides

8Bearings and Navigation

Reading Bearings Two Ships From Port Turning Off Course Finding 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