Solving SSS Triangles

Definition

SSS means “Side, Side, Side”

When we know 3 sides of the triangle, we can find the missing angles.

Solving SSS Triangle

How To Solve SSS Triangle

To solve SSS triangle:

  1. use The Law of Cosines to calculate one of the angles
  2. use The Law of Cosines to find another angle
  3. use angles of a triangle add to 180° to find the last angle

We use the “angle” version of the Law of Cosines:

Solving SSS Triangle Cosinus Rule
Examples

(they are all the same formula, just different labels)

Solving SSS Triangle Example

In this triangle we know the three sides:

a = √3,

b = 1

c = 2

Step 1

Use The Law of Cosines first to find one of the angles. It doesn’t matter which one.

Let’s find angle A first:

cos A = (b2 + c2 − a2) / 2bc

cos A = (12 + 22 − √32) / (2×1×2)

cos A = (1 + 4 − 3) / 4

cos A = ½

A = cos−1(½)

A = 60°

Step 2

Next we will find another side. We use The Law of Cosines again, this time for angle B:

cos B = (a2 + c2 − b2)/2ac

cos B = (√32 + 22 − 12)/(2×√3×2)

cos B = (3 + 4 − 1) / 4√3

cos B = ½ √3

B = cos−1( ½ √3)

B = 30°

Step 3

Finally, we can find angle C by using ‘angles of a triangle add to 180°’:

C = 180° − 30° − 60°

C = 90°

Now we have completely solved the triangle i.e. we have found all its angles.

Learn More

Solving SSA Triangles

Solving SAS Triangles

How To Find if Triangles are Congruent

Finding an Angle in a Right Angled Triangle

Algebra Index

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