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Working Backwards

Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 31 of 44.

If the area is known, the same rule finds a missing side. Write the rule with the area in place and solve for the side.

$A triangle of area 24 with sides 8 and s and 30° between them$

A triangle of area 24 has sides 8 and s with 30° between them: 24 = 1/2×8×s×sin(30°), which is 24 = 2s, so s = 12. With an angle off the tables the board keeps the sine exact, divides by it, and you round at the end.

Challenge

A triangle has area 30 cm². One side is 7 cm, and the angle between that side and the side x is 38°. Find x, 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 AngleWorking BackwardsThe 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 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