All Three Sides
Part of the Triangles section of Coddy's Geometry journey. Lesson 41 of 63.
Knowing any one side of a 30-60-90 triangle, you can find the other two. Work through the short leg: it is the key to the ratio 1 : √3 : 2.
Here the long leg QR, facing the 60° angle at P, is 6×√(3). The long leg is the short leg times √3, so the short leg is 6. Then the hypotenuse is twice the short leg, 12. From the hypotenuse it works the same way: halve it for the short leg, then multiply by √3.
On the stage you can find the sides in either order. Each one is a step with Special right triangle, or Pythagorean theorem once two sides are known.
Challenge
△ABC has a right angle at B and a 30° angle at C. The long leg BC is 5×√(3). Find the other two sides, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingThe Range of the Third SideThe FormulaRecap: The Third Side5The Pythagorean Theorem
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeRecap: The Hypotenuse8Special Right Triangles
The 45-45-90 TriangleLegs from the HypotenuseThe 30-60-90 TriangleAll Three SidesWhich Triangle Is It?Recap: Special Triangles3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterSides as ExpressionsRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg